Question 1

An object propelled from the ground with an initial velocity of 95 ft/s will reach a maximum height of 141.0 ft. If the initial velocity is increased 13%, by what percentage will the maximum height increase? Round percentages to the nearest integer.
A) 13%
B) 28%
C) 2%
D) 22%

Accepted Answer

The maximum height reached by a projectile is proportional to the square of its initial velocity. Increasing the initial velocity by 13% increases the velocity to 1.13 times the original. The square of 1.13 is approximately 1.2769, indicating a 27.69% increase in maximum height, which rounds to 28%.

Question 2

A crash test is performed on a vehicle. The force of the wall on the front bumper is shown in the table. Estimate the impulse and the speed of the vehicle to the nearest whole number (use m = 200 slugs). 
A) impulse: 246,000 velocity: 1230 ft/s
B) impulse: 8200 velocity: 41 ft/s
C) impulse: 10,800 velocity: 54 ft/s
D) impulse: 324,000 velocity: 1620 ft/s

Accepted Answer

The answer of A crash test is performed on a...

Question 3

A baseball pitcher releases the ball horizontally from a height of 5 ft with an initial speed of 120 ft/s. Find the height of the ball when it reaches home plate 60 feet away. Round to two decimal places. (Hint: Determine the time of flight from the x-equation, then use the y-equation to determine the height.)
A) 2.00 ft
B) 1.00 ft
C) 4.00 ft
D) 3.00 ft

Accepted Answer

The answer of A baseball pitcher releases the ball horizontally...

Question 4

A force of 7 pounds stretches a spring 7 inches. Find the work done in stretching this spring 10 inches beyond its natural length.
A)  foot-pounds
B)  foot-pounds
C)  foot-pounds
D)  foot-pounds

Accepted Answer

First, we can use Hooke's Law to find the spring constant of this spring: 
k = F/x = 7 pounds / 7 inches = 1 pound/inch

Then, we can use the formula for the work done by a spring: 
W = (1/2)kx^2

To find the work done in stretching the spring 10 inches beyond its natural length, we plug in x = 10: 
W = (1/2)(1 pound/inch)(10 inches)^2 = 50 foot-pounds

Therefore, the answer is C, 11eaa88b_9198_9d65_a696_73d2a7d12341_TB5869_11 foot-pounds (rounded to two decimal places).

Question 5

A projectile passes overhead, and you attempt to shoot it down with a cannon. When it passes overhead it is traveling horizontally at 100 m/s at an elevation of 1000 m. Your cannon launches shells at 200 m/s, and in this instance you fire just as the projectile passes overhead and at an angle of 60^o. In this scenario the horizontal velocities of the two projectiles are the same. At what elevation will the cannon shell and the other projectile collide? A) They won't collide before the cannon shell hits the ground. B) 971.7 m C) 877.5 m D) 836.7 m

Accepted Answer

The answer of A projectile passes overhead, and you attempt...

Question 6

A certain not-so-wiley coyote discovers that he just stepped off the edge of a cliff. Fourteen seconds later he hits the ground in a puff of dust. How high in meters is the cliff?
A) 1920.8 m
B) 960.4 m
C) 68.6 m
D) 137.2 m

Accepted Answer

The height of the cliff can be calculated using the formula for the distance fallen under gravity: $d = \frac{1}{2}gt^2$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$ on Earth) and $t$ is the time in seconds. Plugging in the values, we get $d = \frac{1}{2} * 9.8 * 14^2 = 960.4$ meters.

Question 7

Where is the center of mass of a region of uniform density bounded by  ?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Where is the center of mass of...

Question 8

When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/4 of the work has been done? [The density of water is 62.4 lbs/ft³.] A) B) C) D)

Accepted Answer

The answer of When pumping water out of a full...

Question 9

A ball is thrown at an angle of  with an initial speed of 25 meters/second. What is its time of flight ? [Assume the ball is thrown from ground level and lands at ground level.]
A) 0.14 seconds
B) 3.13 seconds
C) 1.10 seconds
D) 3.61 seconds

Accepted Answer

The answer of A ball is thrown at an angle...

Question 10

An object is dropped from a height of 140 feet. Another object directly below the first is launched vertically from the ground with an initial velocity of 70 ft/s. Determine when and how high up the objects collide.

Accepted Answer

The answer of An object is dropped from a height...

Question 11

Compute the weight in ounces of an object extending from x = -5 to x = 25 with density  slugs/in. Round answer to nearest whole number.
A) 21 oz
B) 4 oz
C) 86 oz
D) 443 oz

Accepted Answer

The answer of Compute the weight in ounces of an...

Question 12

A water tower is spherical in shape with radius 50 feet, extending from 100 to 200 feet above ground. Compute the work done in filling the tank from the ground.

Accepted Answer

The answer of A water tower is spherical in shape...

Question 13

A 30-foot chain weighs 750 pounds and is hauled up to the deck of a boat. The chain is oriented vertically and the top of the chain starts 30 feet below the deck. Compute the work done.
A) 11,250 foot-pounds
B) 22,875 foot-pounds
C) 375 foot-pounds
D) 33,750 foot-pounds

Accepted Answer

The work done is calculated by integrating the weight of the chain over the distance it is lifted. The weight per foot is 750/30 = 25 pounds/foot. The work done is the integral from 0 to 30 of 25x dx, which equals 33,750 foot-pounds.

Question 14

In a baseball game a base-runner can attempt to advance when a fielder catches a hit ball before it reaches the ground, so long as the runner doesn't leave base before the fielder catches the ball. The fielder then attempts to throw the ball to the base ahead of the runner. If a base-runner can run from 3rd base to home plate in 4.6 sec, how fast must the centerfielder's throw leave his hand if he makes the catch then immediately throws the ball 370 ft from home plate? Assume the base-runner leaves his base at the same instant the centerfielder throws the ball, and that the ball reaches the catcher standing over home plate at the same height from which it was thrown and at the same time the runner would reach the plate. [Hint: This is basically a problem of determining how much initial vertical velocity the ball needs to stay in the air long enough to reach the plate.]
A) 80 ft/sec
B) 74 ft/sec
C) 109 ft/sec
D) 154 ft/sec

Accepted Answer

We can use the formula d = vt + 0.5at^2, where d is the distance (370 ft), a is gravity (-32.2 ft/sec^2), t is the time the ball is in the air, and v is the initial velocity of the ball. We know that the time the ball is in the air is 4.6 sec, because that is how long it takes the runner to reach home plate. We also know that the ball starts at ground level and ends at ground level, so the initial and final vertical velocities are the same.

Plugging in the values we know, we get:

370 = v(4.6) + 0.5(-32.2)(4.6)^2

Solving for v, we get:

v = 109.1 ft/sec

Therefore, the centerfielder's throw must leave his hand at a speed of 109 ft/sec in order to reach home plate at the same time as the runner.

Question 15

When a certain spring is stretched 0.20 m, 7  of work is done. What is the spring's "spring constant"?
A) 350.0 N/m
B) 175.0 N/m
C) 35.0 N/m
D) 17.5 N/m

Accepted Answer

The answer of When a certain spring is stretched 0.20...

Question 16

A cylindrical water tank has a radius of 4 feet and a height of 3.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft³.] A) 14,115 ft-lbs B) 4705 ft-lbs C) 281 ft-lbs D) 7390 ft-lbs

Accepted Answer

The work done to pump the water out is calculated by integrating the weight of each infinitesimally thin horizontal slice of water times the distance it needs to be lifted. The volume of the tank is πr²h = π(4)²(3) = 48π ft³. The weight of the water is 48π * 62.4 lbs. The center of mass of the water is at 1.5 feet, so the work done is 48π * 62.4 * 1.5 = 14,115 ft-lbs.

Question 17

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?
A) 13 ft/s
B)  ft/s
C)  ft/s
D) 0 ft/s

Accepted Answer

The minimum speed a ball must be thrown upward in order to reach a height of 13 feet is the same as the speed it would be traveling right as it hits the ground. Using the formula vf^2 = vi^2 + 2ad where vf=0 (at the highest point), vi is the initial velocity, a is the acceleration due to gravity (-32 ft/s^2), and d is the distance traveled (13 feet), we can solve for vi.

0^2 = vi^2 + 2(-32)(13)
0 = vi^2 - 832
vi^2 = 832
vi = 28.84 ft/s

Since the ball is traveling downward when it hits the ground, the speed it would be traveling right before it hits the ground would be the opposite of the initial velocity, or 28.84 ft/s. Therefore, the minimum speed that the ball must be thrown upward is 28.84 ft/s or approximately 11.11 m/s, which is closest to choice C (11.11 ft/s or 3.39 m/s).

Question 18

A projectile traveling with momentum 4 kg m/s in one direction undergoes an impulse in the opposite direction. The force of the impulse is described as 6000(sin500t) kg m/s² and it is exerted over a time range . What is the object's momentum (in the direction of the impulse) after the impulse? A) 8 kg m/s B) -20 kg m/s C) -19 kg m/s D) 16 kg m/s

Accepted Answer

The answer of A projectile traveling with momentum 4 kg...

Question 19

Starting with the expression for work  , one can change the look of the expression without changing what it represents by dividing the force F by the area it is applied over and multiplying the differential distance dx by that same area. Force divided by area is a pressure (P), and area times the differential distance is a differential volume. Hence one can also describe work as  . A gas at constant temperature will change its pressure inversely to changes in volume,  . If a sample of gas has a pressure of 1 atmosphere when its volume is 1 L, how much work does it do when it expands from 1 L to 3 L?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Starting with the expression for work ...

Question 20

Identify the mass of a thin wire with density  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Identify the mass of a thin wire...

Quiz 6: Applications of the Definite Integral

An object propelled from the ground with an initial velocity of 95 ft/s will reach a maximum height of 141.0 ft. If the initial velocity is increased 13%, by what percentage will the maximum height increase? Round percentages to the nearest integer.

A crash test is performed on a vehicle. The force of the wall on the front bumper is shown in the table. Estimate the impulse and the speed of the vehicle to the nearest whole number (use m = 200 slugs) .

A force of 7 pounds stretches a spring 7 inches. Find the work done in stretching this spring 10 inches beyond its natural length.

A certain not-so-wiley coyote discovers that he just stepped off the edge of a cliff. Fourteen seconds later he hits the ground in a puff of dust. How high in meters is the cliff?

Where is the center of mass of a region of uniform density bounded by ?

When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/4 of the work has been done? [The density of water is 62.4 lbs/ft³.]

A ball is thrown at an angle of with an initial speed of 25 meters/second. What is its time of flight ? [Assume the ball is thrown from ground level and lands at ground level.]

An object is dropped from a height of 140 feet. Another object directly below the first is launched vertically from the ground with an initial velocity of 70 ft/s. Determine when and how high up the objects collide.

Compute the weight in ounces of an object extending from x = -5 to x = 25 with density slugs/in. Round answer to nearest whole number.

A water tower is spherical in shape with radius 50 feet, extending from 100 to 200 feet above ground. Compute the work done in filling the tank from the ground.

A 30-foot chain weighs 750 pounds and is hauled up to the deck of a boat. The chain is oriented vertically and the top of the chain starts 30 feet below the deck. Compute the work done.

When a certain spring is stretched 0.20 m, 7 of work is done. What is the spring's "spring constant"?

A cylindrical water tank has a radius of 4 feet and a height of 3.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft³.]

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?

A projectile traveling with momentum 4 kg m/s in one direction undergoes an impulse in the opposite direction. The force of the impulse is described as 6000(sin500t) kg m/s² and it is exerted over a time range . What is the object's momentum (in the direction of the impulse) after the impulse?

Identify the mass of a thin wire with density .

Quiz 6: Applications of the Definite Integral

An object propelled from the ground with an initial velocity of 95 ft/s will reach a maximum height of 141.0 ft. If the initial velocity is increased 13%, by what percentage will the maximum height increase? Round percentages to the nearest integer.

A crash test is performed on a vehicle. The force of the wall on the front bumper is shown in the table. Estimate the impulse and the speed of the vehicle to the nearest whole number (use m = 200 slugs) .

A force of 7 pounds stretches a spring 7 inches. Find the work done in stretching this spring 10 inches beyond its natural length.

A certain not-so-wiley coyote discovers that he just stepped off the edge of a cliff. Fourteen seconds later he hits the ground in a puff of dust. How high in meters is the cliff?

Where is the center of mass of a region of uniform density bounded by ?

When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/4 of the work has been done? [The density of water is 62.4 lbs/ft3.]

A ball is thrown at an angle of with an initial speed of 25 meters/second. What is its time of flight ? [Assume the ball is thrown from ground level and lands at ground level.]

An object is dropped from a height of 140 feet. Another object directly below the first is launched vertically from the ground with an initial velocity of 70 ft/s. Determine when and how high up the objects collide.

Compute the weight in ounces of an object extending from x = -5 to x = 25 with density slugs/in. Round answer to nearest whole number.

A water tower is spherical in shape with radius 50 feet, extending from 100 to 200 feet above ground. Compute the work done in filling the tank from the ground.

A 30-foot chain weighs 750 pounds and is hauled up to the deck of a boat. The chain is oriented vertically and the top of the chain starts 30 feet below the deck. Compute the work done.

When a certain spring is stretched 0.20 m, 7 of work is done. What is the spring's "spring constant"?

A cylindrical water tank has a radius of 4 feet and a height of 3.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft3.]

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?

A projectile traveling with momentum 4 kg m/s in one direction undergoes an impulse in the opposite direction. The force of the impulse is described as 6000(sin500t) kg m/s2 and it is exerted over a time range . What is the object's momentum (in the direction of the impulse) after the impulse?

Identify the mass of a thin wire with density .

When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/4 of the work has been done? [The density of water is 62.4 lbs/ft³.]

A cylindrical water tank has a radius of 4 feet and a height of 3.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft³.]

A projectile traveling with momentum 4 kg m/s in one direction undergoes an impulse in the opposite direction. The force of the impulse is described as 6000(sin500t) kg m/s² and it is exerted over a time range . What is the object's momentum (in the direction of the impulse) after the impulse?