Kinematics Questions and Answers

2 The graph below shows the relationship between the speed and elapsed time for an object falling freely from rest near the surface of a planet Speed m s 10 01 8 0 6 0 4 0 2 0 0 Speed vs Time 1 0 2 0 3 0 4 0 Time s lculate the slope of this graph to find the rate of acceleration of the free falling object Show the two points that you Ose to use the formula and your answer before rounding as well as the final answer with units

A pilot wishes to fly their aircraft on a bearing of N20 E at a ground speed of 160 km hr There is a wind blowing from the direction N80 E with speed 36 km hr Determine the heading and airspeed that the navigator should use Round answer to the nearest tenth

4 In order to stop quickly on a runway a plane travelling at 220 m s must steadily increase its braking force Suppose the displacement can be represented by the function s t 220t 0 4t a Determine the stopping distance b Determine the maximum breaking deceleration

4 The diagram below illustrates a person who starting from the origin walks 8 km east during first day and 5 km west the next day Use it to answer the following question 4 What is the traveled distance of the person from the initial point in two days 2 1 0 A 13 km B 3 km C 10 km D 5 km 1 2 3 4 5 a D2 6 7 8 2 points 9 10 X km

In problems 20 and 21 you must include the effects of air resi 19 A 0 2 kg rubber ball is dropped from a height of 2 5 meters and then bounces back up to a height of 2 0 much thermal energy was generated as the ball bounced off of the floor mol energy is generated through air

4 A tailback initially running at a velocity of 5 0 m s becomes very tired and slows down at a uniform rate of 0 25 m s How fast will he be running after going an additional 10 meters V S

3 A circus cannon fires an acrobat into the air at an angle of 45 above the horizontal and the acrobat reaches a maximum height y above her original launch height The cannon is now aimed so that it fires straight up into the air at an angle of 90 to the horizontal What is the maximum height reached by the same acrobat now y a b C d e alna sals y 2

A cannon launches a cannonball at 52 m at an angle of 23 above horizontal Assume level ground Calculate of the cannonball the range Lox V 52 A 23

65 52 5732 answered Question 18 An object is thrown upward at a speed of 150 feet per second by a machine from a height of 9 feet off the ground The height of the object after t seconds can be found using the equation s t 16t vot so where is the initial velocity and so is the initial height Give all numerical answers to 2 decimal places a When will the object reach its maximum height b What is its maximum height c When will the object reach the ground feet seconds 0 1 pt 5 seconds

The speed m s of an object is given as a function of time seconds by v t 200ln 1 t t t 0 a Using Euler s method with a step size of 3 seconds find the distance traveled in meters by the body from t 0 to t 9 seconds

d v v t T 2 Dylan Young Type f 1 Zoom Link Parent Graphs Ms Donohue Science BASO Virtual Acade Vf V at C Clever Portal Gmail YouTube Maps mg Fc mac d v t 1 at v ac v v 2ad 12 3 15 pts An arrow is released at an angle of 42 above the horizontal and has a range of 40 m The arrow lands 2 72 seconds later A What was its initial velocity B What was its maximum height

3 Torbjorn was traveling at 50 mph on a concrete road with a drag factor of 1 2 His brakes were working at 96 efficiency To the nearest tenth of a foot what would you expect the average length of the skid marks to be if he applied his brakes in order to come to an immediate stop A 41 6 ft B 78 1 ft C 72 3 ft D 34 6 ft

An airplane flies at 500 mph with a direction of 135 relative to the air The plane experiences a wind that blows 60 mph with a direction of 60 Part A Write each of the vectors in linear form Show all necessary calculations 6 points Part B Find the sum of the vectors Show all necessary calculations 2 points Part C Find the true speed and direction of the airplane Round the speed to the thousandths place and the direction to the nearest degree Show all necessary calculations 7 points

27 A baseball pitcher pitches a ball at a speed of 62 ft s at an angle of 8 above the horizontal from a height of 6 feet The acceleration due to gravity is 32 17 ft s 6 points a After how many seconds will the ball hit the ground Round your answer to the nearest hundredth of a second 4 points 13

2 A clock has a 10 cm second hand From the 12 PM mark to the 9 PM mark for the tip of the second hand calculate the 15 pts a Displacement vector in unit vector notation b Average velocity vector in unit vector notation c Average acceleration vector in unit vector notation d Calculate the magnitude and direction of the instantaneous acceleration at the 3 PM mark se a coordinate system with the origin at center of the clock with the x axis along e 3 PM mark and the y axis along the 12 PM mark Express your answers in units cm sec

c 4 Points Then determine how far the jumper falls during the time period you found in

For problems 4 5 consider the following information When tossing a ball directly upward on earth Jose s fastest throw takes 1 0 s to reach its highest point 4 What speed does Jose throw the ball at a 9 8 m s b 4 9 m s c 50 m s d Impossible to determine 5 If Jose tossed a ball at the same speed on the moon again directly upward how long would it take to reach its highest point Acceleration due to gravity on the moon is 1 6 m s a 1 0 s b 1 6 s c 6 1 s

A 430 kg rocket starts from rest and accelerates to a speed of 12 m s at an angle of 30 with the horizontal within 4 5 s Calculate the net work done on the rocket when it is 123 m above the ground 1 Point O 140 kJ O 160 kJ O 280 kJ O 550 kJ

A disc of mass M 2 kg and radius R 20 cm is connected to a spring at a point at a distance r 10 cm from the centre and a spring constant k 20 N m Find the period of the small oscillations The moment of inertia of the disc is I MR2 The small mass has m 1 kg M m Figure 4

11 The graph in the figure shows the position of a particle as it travels along the x axis What is the magnitude of the instantaneous velocity of the particle when t 1 0 s x m 4 0 2 0 2 0 10 1 0 2 0 3 0 4 0

4 The following table lists the data for the position x versus time t were taken for a block m that is uniformly accelerated Following the example given below to complete the table t s x m 0 000 0 000 Ax m v m s t s 0 100 0 0102 0 050 work below 0 0297 0 297 0 150 V FOMINE 0 200 0 0399 Ar 0 0399 0 0102 0 0297 m At 0 200 0 100 0 100 s Ar 0 0297 At 0 100 Tabel NUE CHE REMOTERS MAGN FESTASE Ale wie 0 300 0 400 0 0896 0 1603 INGRED 0 250 TRIECIE CAFETERA Example The velocity v calculated in this step is the instantaneous velocity at the center of At for example v 0 297 m s is the instantaneous velocity at f 0 150 s the center of 0 100 s and 0 200 s 0 350 0 297 m s 0 500 0 2498 0 450 0 600 0 3607 0 550

3 The velocity of a dragster as it races down a 400 drag strip Determine a approximately how fast the dragster was going after 6s b the approximate velocity of the dragster at the finish line at approximately 9s c the approximate acceleration at the finish line d the displacement after 4s Provide graph of displacement s t e the displacement after 8s 100 v t 80 60 40 20 20 m s N 8 10 12 s S

1 Using 0o 35 and the initial speed vo found above to calculate Vox and Voy Vox Voy Is shot at 06 35 with 2 Using y Voyt 2 ayt to solve for t time of flight in the case that the projectile is fired at 00 350 Recall it is a quadratic equation of t ay g 9 80 m s and y h Show your work here 3 Using X Xo Voxt to find the range of the projectile R x xo This is your predicted range Show your work here

i u and v have an angle of 70 between them ii lul 40 and v 30 iii w u v iv x ux v Find 1 u v 2 The magnitude of the projection of Von u 3 The angle separating the vectors w and u 4 x Blank 1 Blank 2 Blank 3 Blank 1 P PJ

34 A toy rocket is launched upward in the air at 128 feet per second from ground level The height of the ball is modeled by the equation h t 16t 128t where h t is the height of the rocket in feet and t is the time since the rocket was launched in seconds When does the rocket hit the ground

The lob in tennis is an effective tactic when your opponent is near the net It consists of lofting the ball over his head forcing him to move quickly away from the net see the drawing Suppose that you lob the ball with an initial speed of 15 0 m s at an angle of 50 08 above the horizontal At this instant your opponent is 10 0 m away from the ball He begins moving away from you 0 30 s later hoping to reach he ball and hit it back at the moment that it is 2 10 m above its launch point With what minimum average speed must he move Ignore the fact that he can stretch so that his racket can reach the ball before he does

Three balls are launched simultaneously as in the figure The red ball is launched at an initial velocity directed at an angle 8 above the horizontal The blue ball is launched vertically with a speed of 10 1 m s and the yellow ball is launched horizontally with a speed of 4 70 m s The blue and red balls reach identical maximum heights and return to the ground at the same time and the red ball returns to the ground to meet the yellow ball at the same place along the horizontal Find a the launch speed v0 and b the launch angle 8 for the red ball

35 0 A 1 35 m 1 70 m Poil s Auto Repair 3 80m 000 Problem 1 A shop sign weighing 25 kg is supported by a uniform 15 82 kg beam as shown in the figure above on the left The beam is supported by a tension T provided by a cable that makes an angle of 35 with the beam a What is the tension T in the cable Answer 708 1 N b What is N the horizontal component of the force the hinge or pivot exerts on the beam Answer 580 0 N c What is N the vertical component of the force the hinge or pivot exerts on the beam Answer 6 1 N downwards Problem 2 A traffic light hangs from a pole as shown in the figure above on the right The uniform aluminum pole AB is 7 5 m long and has a mass of 12 kg The mass of the traffic light is 21 5 kg a What is the tension T in the horizontal cable CD Answer 425 1 N b What is N the horizontal component of the force the hinge or pivot at point A exerts on the pole Answer 425 1 N c What is Ny the vertical component of the force the hinge or pivot at point A exerts on the pole Answer 328 3 N

A primary focus of this chapter has been projectile motion These ad ditional problems serve as a review of the basic features of this type of motion 81 DA ssm Three balls are launched simultaneously as in the figure The red ball is launched at an initial velocity 7 directed at an angle 0 above the horizontal The blue ball is launched vertically with a speed of 10 0 m s and the yellow ball is launched horizontally with a speed of 4 6 m s The blue and red balls reach identical maximum heights and return to the ground at the same time and the red ball returns to the ground to meet the yellow ball at the same place along the horizon tal Concepts i Since the blue and red balls reach the same maximum height what can be said about the y components of their velocities ii Since the red and yellow balls travel equal distances along the x direction in the same amount of time what can be said about the components of their initial velocities Calculations Find the launch speed and launch angle 0 for the red ball

max 10 0 m s 4 6 m s Problem 81 2 A projectile is launched from and returns to ground level as the gure shows There is no air resistance The horizontal range of the pro ectile is measured to be R 175 m and the horizontal component of the 25 m s Concepts i What is the final value of unch velocity is va he horizontal component v of the projectile s velocity ii Can the time e determined for the horizontal part of the motion iii Is the time for the horizontal part of the motion the same as that for the vertical part iv For the vertical part of the motion what is the displacement of the projectile Calculations Find the vertical component of the projectile 7 25 m s R 175 m T Problem 82

Read lab handout and tex dimensions then answer the following questions y Vo I 1 A ball is fired horizontally along the x axis from the edge of a table as shown above Ignore air resistance what kind of motion of the ball is in the x direction constant velocity zero acceleration or constant but non zero acceleration If its motion has a constant but non zero acceleration please indicated the magnitude and direction of the acceleration 2 A ball is fired horizontally along the x axis from the edge of a table as shown above Ignore air resistance what kind of motion of the ball is in the y direction constant velocity zero acceleration or constant but non zero acceleration If its motion has a constant but non zero acceleration please indicated the magnitude and direction of the acceleration

45 X 3 A ball is fired at an angle 0o 45 relative to the horizontal x axis from the edge of a table fo as shown in the figure above Ignore air resistance what kind of motion of the ball is in the x direction constant velocity zero acceleration or constant but non zero acceleration If its motion has a constant but non zero acceleration please indicated the magnitude and direction of the acceleration 4 A ball is fired at an angle 80 45 relative to the horizontal x axis from the edge of a table as shown in the figure above Ignore air resistance what kind of motion of the ball is in the y direction constant velocity zero acceleration or constant but non zero acceleration If its motion has a constant but non zero acceleration please indicated the magnitude and direction of the acceleration

A bat flying in a cave emits a sound and receives its echo 2 3 s later How far away is the cave wall if the speed of sound is 343 m s

The ray diagram shows a vase that is placed beyond the center of curvature of a concave mirror Which best describes how the image of the vase will appear C F O It will be larger than the vase and upright It will be smaller than the vase and upright It will be larger than the vase and inverted OIt will be smaller than the vase and inverted

For time t 0 the velocity of a particle moving along the x axis is given by v t sin e0 3t The initial position of the particle at time t 0 is x 1 25 What is the displacement of the particle from time t 0 to time t 10 10 points U Font Family AA

Sahib slides a 1 5 kg drill down on a sloped roof It slides down the roof to a level portion of the roof where it slides another 2 5 m along this horizontal surface The coefficient of friction between the drill handle and the shingles is 0 850 a Draw a free body diagram of the drill as it slides across the level portion of the roof 1 mark b Calculate the amount of kinetic friction acting on the drill 2 marks c Calculate the work done by the kinetic friction 2 marks

A bead with a hole through it slides on a wire track The wire is threaded through the hole in the bead and the bead slides without friction around a loop released from rest at a height h 3 00R a What is its speed at point A Use the following as necessary the acceleration due to gravity g and R 2gR V R b How large is the normal force on the bead at point A if its mass is 5 70 grams 111 72 XN downward B magnitude direction c What If What is the minimum height h from which the bead can be released if it is to make it around the loop Use any variable or symbol stated above as necessary 5R h 2 I X

13 The object is pulled upward at constant speed

A ball is thrown vertically upward from the top edge of a building 250 m tall with an initial velocity of 25 m s Assume the acceleration due to gravity is g 10 ms 2 How long will it take for the ball to rise to the highest point on its trajectory AF one decimal place QUESTION 2 What is the maximum height measured from the ground to which the ball rises AF two decimal places QUESTION 3 What is the magnitude of the velocity with which the ball hits the ground AF no decimals

3 A 4 0 x 10 N Truck moving west at a velocity of 8 0 m s collides with a 3 0x10 N truck heading south at a velocity of 5 0 m s If these two vehicles lock together upon impact what is their velocity 5 0 m s 25 S of W

NIT 5 Momentum and Collisions 3 The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition nowadays the ballistic pendulum has been replaced by the ballistic chronograph an electronic device The ballistic pendulum is a simple pendulum that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet into the pendulum bob Let L 1 6 m and mA 5 5 kg For a certain historical pistol which fired a roundball of mass me 91 g it is found that the maximum swing angle of the pendulum is 52 Determine the pre impact speed of the bullet B T6 C4 L B VERSION 14 0

4 Bodies A and B are moving in the same direction in a straight line with a constant velocities on a frictionless surface The mass and the velocity of A are 2kg and 10 m s The mass and the velocity of B are 6kg and 4 m s A spring is connected to the back of the body B who s spring constant is 800 N m What would the maximum compression of the spring be T6 C4 A 10 m s 2 kg B 4 m s 6 kg

2 Two cars both with mass m collide and stick together Prior to the collision one car had been travelling north at a speed of 2v while the second was travelling at a speed v at an angle as shown on the diagram After the collision the two cars travel with a Vfinal at an angle NORTH EAST again as shown in the figure Determine the final velocity if v 25 m s and 30 T6 C4 Z II E 2v Vfinal

a Velocity m s a Position m 50 b 40 30 20 50 40 30 10 20 10 0 describe what the graph says about the object s motion Use for 9 as well 1 A 2 2 1 B Use for 8 as well 1 3 4 Time s 5 6 Use for 10 as well a m s C 2 3 Time s 7 8 4 5 t s

Two mechanical waves whose pulses are on the same side meet What kind of interference occurs Select one O a constructive O b complete destructive C none O d destructive

The velocity of an object undergoing a constant acceleration is shown at two different times The velocity at the early time is v the velocity at the later time is v What is the direction of the acceleration O A OB D V V A B X C D E None of these Some other direction or acceleration is zero

A drone carrying two identical packages moves straight up and when it reaches height h it hovers above the ground The drone malfunctions ejecting package A downward at a speed vo and package B upward at the same speed Ignore air resistance a How do the landing velocities of the packages compare VA VB VA VB Justify your answers without deriving equations VA VB

Dylan Young Type Zoom Link Parent Graphs Ms Donohue Science BASD Virtual Acade C Clever Portal Gmai There is a second hot spot in the lower right corner of the iFrame Dragging this hot spot allows you to change the size of iF dimensions you prefer A ball is launched at an angle Its location at 1 s intervals is shown Rank the three indicated locations based on their horizontal speed vx and vertical speed vy C E A Middlest B D Tap table cells to toggle through answer options Vx Smallest Vy Smallest Middlest 5 OH d young student Student N org Activity Horizontal and Ve Progress F 1 4 2 5 Tap for Question S

Mort stands on Earth Velma moves away from him in a rocket at 299 000 km s 1000 km s slower than lightspeed Mort sends a laser beam toward Velma As the tip of the beam passes her rocket Mort observes a the beam moving away at 300 000 km s b the beam moving just 1000 km s faster than Velma c the beam both of the above d the beam moving 300 000 km s faster than Velma e all of the above

For both Tracker experiments calculate the average vertical acceleration where the time period is t 0 10 second to t 1 00 second Consider only the magnitude of the vertical velocity in the calculations Record your results to three significant figures Comment How does the average acceleration of the two balls compare to the theoretical value of 9 81 meters second and how do the accelerations of the two balls compare to each other BIU x E 33 0 small ball large ball O X Font Sizes T A 1 36 M A Initial Vertical Velocity at t 0 10 1 32 Final Vertical Velocity at t 1 00 9 61 9 07 a Av At 0 0