Kinematics Questions and Answers

A cannon having a muzzle speed of 1000 m/s is used to destroy a target on a mountaintop. The target is 2000 m from the cannon horizontally and 800 m above the ground. At what angle, relative to the ground, should the cannon be fired?

You are an astronaut on the surface of a newly discovered planet. In an attempt to determine the acceleration due to gravity on this planet, you use a spring-loaded launcher to fire a steel marble straight upward. 1.68 seconds after firing, the marble hits the ground. If the spring-loaded launcher fired the marble with an initial velocity of 11.5 m/s, the magnitude of the acceleration due to gravity on this planet must be m/s².

A pitcher throws an overhand fastball from an approximate height of 2.65 m and at an angle of 2.5° below horizontal. The catcher catches the ball high in the strike zone, at a height of 1.02 m above the ground. If the pitcher's mound and home plate are 18.5 m apart, what is the initial velocity of the pitch?

A physics archer shoots an arrow vertically upwards beside a building 56 m high. The arrow's initial velocity is 37 m/s. If air resistance is negligible, at what time does the arrow pass the top of the building on its way up and down?

A speed skater moves at a steady 7 m/s across smooth ice. She hits a 4.0 meter wide rough patch and slows to 5.5 m/s. What was her acceleration on the rough ice? Assume a constant acceleration.

I was walking in the woods behind our neighborhood park with my 2-year-old, Willow. She started lagging behind, and suddenly I heard her shout "Look!" I turned around to find her 20 meters behind me, reaching for a beehive that had fallen on the ground. It took me about 1/4 of a second to react, and then I took off with an acceleration of 2.5 m/s² for 1 second, before running out of steam and continuing at a constant speed. How much time passed between when she shouted and when I reached her?

A physics student has a pea-shooter that, when he exhales rapidly, can fire peas at an initial velocity of 18.0 m/s. If he holds the pea shooter at an angle of 24.0° above horizontal and 1.95 m above the ground, calculate: a. the time spent by the pea in the air. b. the range of the pea. c. the maximum height of the pea.

A person decides to swim across a river 84 m wide that has a current moving with a velocity of 0.40 m/s [E]. The person swims at 0.70 m/s [N] relative to the water. a. What is the velocity of the person with respect to the Earth? b. How long will it take to cross the river? c. How far downstream will the person land? d. In what direction should the person swim if they want to land at a point directly north of where they started?

On a field goal attempt, a kicker must kick a football from a spot 36.0 m away from the goal line and the ball must clear the crossbar 3.05 m high. When kicked, the ball leaves with an initial velocity of (12^i +16 "j) m/s. a. By how much does the ball clear or fall short of the cross bar? b. Does the ball approach the crossbar while still rising or while falling?

Find the total displacement or velocity for the following cases: 1) A bee flies 12 m north, 8 meters west, and then 4 meters south. What is the displacement of the bee? 2) A person walks 6 blocks south, 4 blocks west and then 6 blocks north. What is the person's displacement in blocks? 3) A boat that moves with a constant velocity of 12 m/s, North is on a river with a constant current of 4 m/s South. What is the resultant velocity of the boat? 4) An airplane travels with a constant velocity of 210 m/s, East and in the upper atmosphere where the plane is traveling there is a wind that is blowing at a constant velocity of 60 m/s to the east. What is the resultant velocity of the boat?

A tennis ball is dropped from 1.86 m above the ground. It rebounds to a height of 0.921 m. With what velocity does it hit the ground? The acceleration of gravity is 9.8 m/s². (Let down be negative.) Answer in units of m/s.

An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 110 m from the crossing and its speed is 25 m/s. If the engineer's reaction time is 0.2 s, what should be the magnitude of the minimum de- celeration to avoid an accident? Answer in units of m/s².

In a test run, a certain car accelerates uniformly from zero to 24.0 m/s in 2.95 s. (a) What is the magnitude of the car's acceleration? (b) How long does it take the car to change its speed from 10.0 m/s to 20.0 m/s? (c) Will doubling the time always double the change in speed? Why?

A reconnaissance plane flies 433 km away from its base at 332 m/s, then flies back to its base at 498 m/s. What is its average speed? Answer in units of m/s.

The engine of a locomotive exerts a constant force of 6.6 x 10^5 N to accelerate a train to 90 km/h. Determine the time (in min) taken for the train of mass 1.1 x 10^7 kg to reach this speed from rest.

A golfer on a fairway is a horizontal distance of 85 m away from the green, which sits below the level of the fairway by 25 m. If the golfer hits the ball at an angle of 35° with respect to the horizontal, and with an initial speed of 21 m/s, how close to the green does she come? (Find the distance, in meters, from the ball to the green. Assume the area on which the ball lands is level with the green, and assume the ball does not bounce or roll.)

You drive a car 630 ft to the east, then 330 ft to the north. What is the magnitude of your displacement? What is the direction of your displacement?

A girl delivering newspapers covers her route by traveling 4.00 blocks west, 3.75 blocks north, and then 7.50 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

Chrissy was twirling her pencil and accidently dropped it from a height of 0.8 m. a) How long does Chrissy have to grab her pencil before it hits the tile floor? Use the formula d= ½gt² and solve for t. The acceleration due to gravity (g) is 9.8 m/s². b) How fast is the pencil traveling before it hits the floor? (Round to the nearest tenth). Use the formula Vf = Vi + at, where V; is the initial velocity, a is the acceleration, and t is the time.

An object begins with an initial velocity of 5.56 m/sec and accelerates for 4.45 seconds at a rate of 3.24 m/sec². What is its final velocity? Your answer: 19.98 m/s 24.50 m/s 34.77 m/s 46.54 m/s

You and a friend each drive 57 km to the same destination. You travel at 89.6 km/h and your friend at 96.8 km/h. How long will your friend wait for you at the end of the trip? Answer in units of min.

Maria decides to check if the speedometer on her car is working properly. She drives so that her speedometer reads a constant 70 mph. She then records the time it takes to drive between successive mile markers, spaced exactly 1.00 mile apart, to be 55 seconds. Is her speedometer accurate? Explain your answer

Certain insects can achieve seemingly impossible accelerations while jumping. The click beetle accelerates at an astonishing 400g over a distance of 0.58 cm as it rapidly bends its thorax, making the "click" that gives it its name. How much time is required for the beetle to reach this speed? Ignoring air resistance, how high would it go?

A fastball pitcher can throw a baseball at a speed of 41 m/s (92 mi/h). (a) Assuming the pitcher can release the ball 16.5 m from home plate so the ball is moving horizontally, how long (in s) does it take the ball to reach home plate? (b) How far (in m) does the ball drop between the pitcher's hand and home plate? (Enter the magnitude.)

IP A white-crowned sparrow flying horizontally with a speed of 1.90 m/s folds its wings and begins to drop in free fall. How far does the sparrow fall after traveling a horizontal distance of 0.400 m? If the sparrow's initial speed is increased, does the distance of fall increase, decrease, or stay the same?

At t = 10 s, a particle is moving from left to right with a speed of 5.0 m/s. At t = 20 s, the particle is moving right to left with a speed of 6.8 m/s. Assuming the particle's acceleration is constant, determine the following. (Assume the positive direction is to the right.) (a) its acceleration (Enter your answer in m/s2. Indicate the direction with the sign of your answer.) (b) its initial velocity (Enter your answer in m/s. Indicate the direction with the sign of your answer.) (c) the instant (in s) when its velocity is zero

A ball is rolling up a ramp with an initial velocity of +4.0 m/s at t=0 seconds and a constant acceleration of -2.0 m/s^2. What can be said about the ball's direction of travel and speed at t = 5 seconds? Choose 1 answer: A The ball's direction is positive, and the speed is increasing. B The ball's direction is negative, and the speed is increasing. C The ball's direction is negative, and the speed is decreasing. D The ball's direction is positive, and the speed is decreasing.

Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15-min lead on the slower car?

A 0.40 kg toy car moves at constant acceleration of 2.3 m/s². Determine the net applied force that is responsible for that acceleration. a. What is the mass of the toy car? b. What is the acceleration of the toy car?

On Planet X a 0.5 kg space rock falls a distance of 2.5 meters and loses 20 J of energy. What is the gravity on Planet X? a. How much energy was lost? b. What is the mass of the space rock? c. What distance did the space rock fall?

The infamous chicken is dashing toward home plate with a speed of 6.0 m/s when he decides to hit the dirt. The chicken slides for 1.2 s, just reaching the plate as he stops (safe, of course). What is the magnitude of the chicken's acceleration? Express your answer using two significant figures. What is the direction of the chicken's acceleration? opposite the direction of motion along the direction of motion

Consider the following problem. Find the distance traveled in 50 seconds by an object traveling at a velocity of v(t) = 20 + 7cos(t) feet per second. Decide whether the problem can be solved using precalculus, or whether calculus is required. The problem can be solved using precalculus. The problem requires calculus to be solved. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. (Round your answer to the nearest foot.)

It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this week. She must get from one side of the school to the other by hurrying down three different hallways. She runs down the first hallway, a distance of 35 m, at a speed of 3.4 m/s. The second hallway is filled with students, and she covers its 48-m length at an average speed of 1.2 m/s. The final hallway is empty, and Suzette sprints its 60-m length at a speed of 5.1 m/s. How long does it take her to get to class? (Express your answer in seconds.)

A train is moving parallel and adjacent to a highway with a constant speed of 23 m/s. Ini- tially a car is 59 m behind the train, traveling in the same direction as the train at 35 m/s and accelerating at 4 m/s². What is the speed of the car just as it passes the train? Answer in units of m/s.

HOW MANY of the identified objects are NOT accelerating? a race car going around a circular track at 150 MPH a sky diver falling at a constant speed a heavy box sliding across the floor, after being released a bowling ball colliding with a pin a vibrating guitar string a baseball flying through the air a child swinging on a swing

1. An Indy-500 race car's velocity increases from 4.00 m/s to 36.0 m/s over an interval lasting 4.00 seconds. What is the car's average acceleration? How far does the car travel during this amount of time? (8 m/s2, 64m)

This time particle A starts from rest and ac- celerates to the right at 56.3 cm/s². Particle B starts 358 cm down the track and moves at a constant velocity of 40.6 cm/s to the left. When will they meet? Answer in units of s.

* 8. In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due turns around, and hikes with an average velocity of 0.447 m/s, due east. How far east did she walk? west,

A 45 kg swimmer starting from rest can develop a maximum speed of 12 m/s over a distance of 20 m. How much net force must be applied to do this? What is the distance covered by the swimmer? b. What is the mass of the swimmer? c. What is the speed of the swimmer?

You are driving through town at 14.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and begin decelerating at 3.2 m/s². Find the speed of your car when you have traveled half the distance in part A. Express your answer to three significant figures.

(10%) Problem 3: A skydiver falls d₁ = 435 meters in t₁ = 8.6 s before opening his parachute. After the chute opens, he falls an additional d₂ = 895 meters in t2 = 137 s. See the figure.

You ride in a boat on a river flowing at 1.2 m/s (in the negative y direction). Suppose you would like the boat to move directly across the river (in the positive x direction) with a speed of 4.7 m/s. What is the corresponding speed of the boat's velocity relative to the water? Express your answer to two significant figures and include appropriate units.

In this problem, you will apply kinematic equationsto a jumping flea. Take the magnitude of free-fall acceleration to be 9.80 m/s². Ignore air resistance. How long is the flea in the air from the time it jumps to the time it hits the ground? Express your answer in seconds to three significant figures.

The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 49 m in a straight line, reaching a final speed of 95 km/h. (a) Determine the cheetah's average acceleration during the short sprint. (b) Find its displacement at t= 3.0 s. (Assume the cheetah maintains a constant acceleration throughout the sprint.)

A large rock is dropped from the top of a high cliff. Assuming that air resistance can be ignored and that the acceleration has a constant value of 10 m/s², (a) How fast would the rock be traveling 5.7 seconds after it is dropped? (b) What is the speed in MPH?

A cyclist rides 4.8 km east for 24 minutes, then he turns and heads west for 6 minutes and 1.2 km. Finally, he rides east for 7.6 km, which takes 38 minutes. (Assume motion toward the east is positive. Indicate the direction with the signs of your answers.) (a) What is the final displacement of the cyclist (in km)? (b) What is his average velocity (in km/h)?

A ball rolls off a platform that is 8.6 meters above the ground. The ball's horizontal velocity as it leaves the platform is 7.3 m/s. (a) How much time does it take for the ball to hit the ground? (b) How far from the base of the platform does the ball hit the ground? Use g = 10 m/s²

A steel ball is dropped from a diving platform (with an initial velocity of zero). Using the approximate value of g = 10 m/s² (a) Through what distance does the ball fall in the first 0.4 seconds of its flight? (b) How far does it fall in the first 8.2 seconds of its flight?

Part 1: Your ship can sail 10 squares/month. Starting from Spain and travelling west (or bearing 270), draw one vector for each month of travel using your red pencil. In what country will you make landfall? How many months will it take to reach land (how many 10-square vectors is it?

On a drive from your home to town, you wish to average 48 mph. The distance from your home to town is 98 miles. However, at 49 miles (half way), you find you have averaged only 36 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 48 mph? Answer in units of mph.