# Heights and Distances Questions and Answers

Math

Heights and DistancesWhen an object is dropped from a 1515 ft tower, the height of the object in feet after t seconds is given by the function f(t)= - 16t2 + 1515. Find the height of the object after 9 seconds.
The height of the object after 9 seconds is feet.

Math

Heights and DistancesThe trip back took 26 hours. What is the speed of the boat in still water? What is the speed of
A boat traveled 520 miles each way downstream and back. The trip downstream took 13 hours.
the current?

Math

Heights and DistancesThe quadratic function that approximates the height of a javelin throw is below.
Where t is the time in seconds after it is thrown and h is the javelin's height in feet.
How long will it take for the javelin to hit the ground.
h(t) = −0.08ť² + 4. 48
About 56 seconds
About 5.3 seconds
About 7.5 seconds
About 28 seconds

Math

Heights and DistancesFind the distance between the two points listed below. Round to the nearest tenth.
a. A(2, 5) and B(1,8)
b. A(-4, 6) and B(-2,-2)
c. A(8, 3) and B(9, -3)

Math

Heights and DistancesA river flows northward at 7 miles per hour. A boat crosses westward at 3 miles per hour.
a. Draw a diagram that shows the boat's resultant velocity in the river.
b. Write vectors for the river (r) and boat (b), and boat's resultant velocity in the river in component
form:
r=
b =
r+b=
c. What is the speed of the boat in the river?

Math

Heights and DistancesA water trough is 800 cm long and a cross-section has the shape of an
isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at
the top and has a height of 50 cm.
If the trough is being filled with water at the rate of 18000 cm³/min,
how fast (in cm/min) is the water level rising when the water is 30 cm
deep?
Note: Round to the nearest thousandth.

Math

Heights and DistancesA boat is pulled in to a dock by a rope with one end attached to the
front of the boat and the other end passing through a ring attached to
the dock at a point 12 ft higher than the front of the boat. The rope is
being pulled through the ring at the rate of 0.21 ft/sec.
How fast (in ft/s) is the boat approaching the dock when 13 ft of rope
is out?
Note: Round to the nearest hundredth. Speed is always positive.

Math

Heights and DistancesHow high is a tree that casts a 32-ft shadow at the same time a 6-ft pole casts a shadow which is 10 ft long?
The tree's height is
(Round to the nearest tenth, if necessary.)

Math

Heights and DistancesA classic physics problem states that if a projectile is shot vertically up into the air with an initial velocity of 198 feet per second from an initial height of 108 feet off the ground, then the height of the projectile, h, in feet, t seconds after it's shot is given by the equation:
h = -16t² + 198t + 108
Find the two points in time when the object is 143 feet above the ground. Round your answers to the nearest hundredth of a second (two decimal places).
Answer: The object is 143 feet off the ground at the following times:

Math

Heights and DistancesA forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3033-foot mesa. In 6 minutes, the angle of depression to the leading edge of the fire changes from 10.9° to 12.29º.
How many feet does the fire advance during the 6 minutes that the ranger is observing it?
(Round your answer to two decimal places.)
At what speed (in MILES PER HOUR) is the fire spreading towards the ranger?
(Round your answer to two decimal places.)

Math

Heights and DistancesAt a point on the ground 12 ft from the base of a tree, the distance to the top of the tree is 3 ft more than 2 times the height of the tree. Find the height of the tree.
The height of the tree is
(Simplify your answer. Round to the nearest foot as needed.)

Math

Heights and DistancesThe radius of the wheel on a car is 24 inches. If the wheel is revolving at 330 revolutions per minute, what is the linear
speed of the car in miles per hour?
Round your answer to the nearest tenth.

Math

Heights and DistancesIron is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron were developed by an institute of medicine for a certain region. The recommended dietary allowance (RDA) of iron for adult females
under the age of 51 years is 16 milligrams (mg) per day. A hypothesis test is to be performed to decide whether adult females under the age of 51 years are, on average, getting less than the RDA of 16 mg of iron per day. Complete parts (a)
through (c).
a. Determine the null hypothesis.
Ho: HV mg
(Type
a decimal. Do not round.)

Math

Heights and DistancesAs shown in the diagram below, the angle of elevation
from a point on the ground to the top of the tree is 34°.
34°
If the point is 20 feet from the base of the tree, what is
the height of the tree, to the nearest tenth of a foot?
A) 29.7 B) 16.6 C) 13.5 D) 11.2

Math

Heights and DistancesBase your answer to the following question on The NuFone Communications Company must run a telephone line between two poles at opposite ends of a lake, as shown in the accompanying diagram. The length and width of the lake are 75 feet and 30 feet, respectively.
What is the distance between the two poles, to the nearest foot?
A) 105
B) 81
C) 69
D) 45

Math

Heights and Distances6) From an airplane flying at a constant altitude over the ocean, the angle of depression to a tugboat is 24". At the same
moment the angle of depression to a ship is 17 and the distance from the ship to the plane is 9120 feet. Find the distance
from the ship to the tugboat.

Math

Heights and DistancesTwo observers are 2.4 miles apart on opposite sides of a hot-air balloon. The angle of elevation from observer A is 30° and the angle of elevation from
observer B is 35. Find the alitude of the balloon to the nearest tenth of a mile.
. Write your answer as a number only.
Round answer to one decimal place.
Answer
Answer

Math

Heights and DistancesTamika is 1.25 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 33.05 meters. She stands 28.9 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Math

Heights and DistancesIf h= - 16t² + 112t represents the height of a rocket, in feet, t seconds after it was fired, when will the rocket hit the ground? (Hint: The rocket is on the ground when h=0)

Math

Heights and DistancesA car travels 80 mi averaging a certain speed. If the car had gone 40 mph faster, the trip would have taken 1 hr less. Find the car's average speed.

Math

Heights and DistancesA parachutist's rate auring a free fall reaches 198 kilometers per hour.
What is this rate in meters per second? At this rate, how many meters
will the parachutist fall during 10 seconds of free fall? Do not round your
answers.

Math

Heights and DistancesA surveying crew has two points A and B marked along a roadside at a distance of 400 yd. A third point C is marked at the back corner of a property along a perpendicular to the road at B. A straight path joining C to A forms a 28° angle with the road. Find the distance from the road to point C at the back of the property and the distance from A to C using sine, cosine, and/or tangent. Round your answers to three decimal places.

Math

Heights and Distances2. To measure the height of Lincoln's caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are taken. If the angle of elevation to the bottom of Lincoln's face is 32° and the angle of elevation to the top is 35°, what is the height of Lincoln's face?

Math

Heights and DistancesFind the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. Use a calculator to estimate the square root to one decimal place.
The length of the leg a is approximately_______ inches.

Math

Heights and DistancesUse the law of sines to solve the given problem..
The loading ramp at a delivery service is 10.5 ft long and makes a 19.0° angle with the horizontal. If it is replaced with a ramp 20.5 ft long, what angle does the new ramp
make with the horizontal?
The new ramp makes a ° angle with the horizontal.
(Round to one decimal place as needed.)

Math

Heights and DistancesScientists believe that the star Sirius (known as the Dog Star) is approximately 81.5 trillion kilometers from the earth. (Round your answers to one decimal place.)
(a) How far, in astronomical units, is Sirius from the earth?
(b) How far, in light-years, is Sirius from the earth?
light-years
(c) How far, in parsecs, is Sirius from the earth?
parsecs

Math

Heights and DistancesA jewelry maker works 6 days a week, makes 15 necklaces per day on average, and charges $18 a necklace. If she lowers her price to $10 a necklace, by how many necklaces per day on average must she increase her production to make the same amount of money per 6-day workweek?

Math

Heights and DistancesUse z scores to compare the given values.
The tallest living man at one time had a height of 243 cm. The shortest living man at that time had a height of 123.6 cm. Heights of men at that time had a mean of 173.66 cm and a standard deviation
of 7.75 cm. Which of these two men had the height that was more extreme?
Since the z score for the tallest man is z = and the z score for the shortest man is z = the man had the height that was more extreme.
(Round to two decimal places.)

Math

Heights and DistancesA hawk is hunting from the air. The hawk is 78 feet high and spots a rabbit that is a horizontal distance of 50 feet away. At what angle is the hawk looking down?

Math

Heights and DistancesIf a runner jogs 2 miles east and then jogs 4 miles north, how far is the runner from her starting point if she plans to run straight back? Remember to simplify your answer.
2√/10
√18
√6
2√5
5√4

Math

Heights and DistancesJim's speedboat can travel 21.5 miles upstream against a 3-mph current in the same amount of time it travels 24.5 miles downstream with a 3- mph current speed. Find the speed of Jim's boat. Speed: mph help (numbers)

Math

Heights and DistancesThe height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 21.5 m/s is h = 2 + 21.5t - 4.9t2 after t seconds.
(a) Find the velocity (in m/s) after t seconds.
v(t) = 1.9
Find the velocity (in m/s) after 2 seconds and after 4 seconds.
v(2) = 1.9
m/s
m/s
V(4) = -17.7
(b) What is the value (in m/s) of v(t) when the projectile reaches its maximum height?
v(t)
m/s
= 2.19
When (in s) does the projectile reach its maximum height? (Round your answer to two decimal places.)
S
(c) What is the maximum height (in m)? (Round your answer to two decimal places.)
25.58
m
(d) When (in s) does it hit the ground? (Round your answer to two decimal places.)
S
(e) With what velocity (in m/s) does it hit the ground? (Round your answer to two decimal places.)
m/s

Math

Heights and DistancesQuestion
On a grandfather clock, the pendulum arm swings a length of 1.4 feet each second.
If the length of the pendulum is 4 feet, what is the measure of the central angle that
intercepts the arc?
2.86 radians
5.6 radians
35 radians

Math

Heights and DistancesRiley bought a child admission ticket and
6 funland ride tickets. He used a coupon for a
$5 discount. Which expression shows Riley's
total cost?
A $12+ (6 × $2)
B
$12 + ($6+$2) - $5
C$12+(6xX $2) - $5
D$12+ (6 × $2) + $5

Math

Heights and DistancesBeatrice is using a cylinder shape container to hold 52 in³ of liquid. The height of the container is 4 inches tall.
What is the best approximation for the radius of the container?
O2.0 in.
O 2.5 in.
O 3.4 in.
6.5 in.

Math

Heights and DistancesAiden borrows a book from a public
library. He read a few pages on day one.
On day
two, he reads twice the number of pages
than he read on day one. On the third day,
he reads six pages less than what he read
on the first day. If he has read the entire
book that contains 458 pages, how many.
pages did he read on day three?
O 104
O 110
120
O229
O 150

Math

Heights and DistancesA street light is at the top of a pole that is 10 feet tall. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the length of her shadow moving when she is 15 ft from the base of the pole?

Math

Heights and DistancesThe angle of elevation to a balloon is 12°. If the balloon is directly above a point 10 kilometers away, what is the altitude of the balloon?

Math

Heights and DistancesSolve the problem.
A building 150 feet tall casts a 60 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle
between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the
top of the building.)
68⁰
24°
66°
22°

Math

Heights and Distances7. A ship drops anchor in a harbor. The anchor is 49 ft. above the surface of the water when it is released. Use the vertical motion formula for height of the anchor, h(t) = -16t² + 49 to answer the following questions.
a. What is the starting height (y-intercept)?
b. What is the value of h when the anchor hits the water?
c. After how many seconds will the anchor hit the water?

Math

Heights and DistancesA kayak is seen floating down a creek. The kayak is first spotted 65 feet away. 9 seconds later the kayak is 15 feet away, making a 30 angle between the two sightings. How far did the kayak travel? Round to the nearest tenth.

Math

Heights and DistancesTo determine the distance between two points A and B, a surveyor chooses a point C that is 215 yards from A and 565 yards from B. If <BAC has measure 49°30', approximate the distance between A and B. (Round your answer to the nearest whole number.)

Math

Heights and Distances[10pts.] A guy wire 77.4 m long is attached to top of an antenna mast that is 71.3 m high. Find the angle (of elevation) that the wire is making with the ground? Apply the appropriate significant digit rules

Math

Heights and DistancesTwo docks are located on an east-west line 2589 ft apart. From dock A, the bearing of a coral reef is 60°22'. From dock B, the bearing of the coral reef is 330°22. Find the distance from dock A to the coral reef.
The distance from dock A to the coral reef ft.

Math

Heights and DistancesRyann and Lydia are taking canoe ride across Smithville lake. They can go 14 miles across the lake in the same time it takes them to go 9 miles back against the current. If their speed in still water is 6mph, What is the rate of the current? Round your answer to the nearest tenth.Type your answer...

Math

Heights and DistancesClaire and Tate travel by plane to Orland. They notice that it takes a total of 5 hours to travel the 2100 miles round trip. If the plane flies at a constant rate of 525mph, what is the speed of the wind? Upload your solution. Provide all work that justifies your solution.

Math

Heights and DistancesSome creep dressed as a clown shot into a crowd at a carnival from a 30-story building 211 feet away. He hit a woman in the head about 5 feet above the ground. The angle determined by investigators was 40 degrees. Draw a picture of the "scene" in the space provided. Make sure to include the triangle and all measurements that you know. Then calculate the height of the shooter in feet. Show your work and circle your answer.

Math

Heights and DistancesCorners are sliced of a unit cube so that the six faces become a regular octagon. The total volume of the removed tetrahedron is V. Then [100 V] is equal to ([.] represents greatest integer function).