Question 1

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration?

Accepted Answer

The only force acting on the projectile in the horizontal direction is the initial velocity. Thus, there is no acceleration in the horizontal direction. Therefore, the horizontal component of the projectile's acceleration is 0 m/s^2.

Question 2

Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of diameter 60 m. What are the magnitude and direction of her acceleration?

Accepted Answer

The answer of Sarah drives at a constant speed of...

Question 3

A child sits on a merry-go-round, 1.5 meters from the center. The merry-go-round is turning at a constant rate, and the child is observed to have a radial acceleration of 2.3 m/s². How long does it take for the merry-go-round to make one revolution?

Accepted Answer

The answer of A child sits on a merry-go-round, 1.5...

Question 4

A disk-shaped space station 125 m in diameter spins at a uniform rate about an axis through its center and perpendicular to the plane of the disk. If the acceleration of a point on the rim of the disk is to be equal to g, how long does it take for the station to make one revolution? Use g = 9.8 m/s².

Accepted Answer

The answer of A disk-shaped space station 125 m in...

Question 5

A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation. What is the acceleration of that point due to the spin of the wheel?

Accepted Answer

The answer of A point on a wheel of radius...

Question 6

You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning. What should be the diameter of this wheel?

Accepted Answer

The answer of You need to design a wheel for...

Question 7

An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?

Accepted Answer

The answer of An object moves with a constant speed...

Question 8

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive?

Accepted Answer

The answer of A jet plane flying 600 m/s experiences...

Question 9

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

Accepted Answer

The answer of A race car traveling at a constant...

Question 10

A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30° above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air resistance?

Accepted Answer

The answer of A rock is thrown from the roof...

Question 11

A 5.0-kg stone is thrown upward at 7.5 m/s at an angle of 51° above the horizontal from the upper edge of a cliff, and it hits the ground 1.5 s later with no air resistance. Find the magnitude of its velocity vector just as it reaches the ground.

Accepted Answer

The answer of A 5.0-kg stone is thrown upward at...

Question 12

A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance,

Accepted Answer

The range of a projectile (the horizontal distance it travels) is proportional to the initial velocity squared, as long as air resistance can be neglected. Therefore, if the initial velocity is doubled, the range will be quadrupled (2^2 = 4).

Question 13

A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s²?

Accepted Answer

The answer of A hobbyist launches a projectile from ground...

Question 14

A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal) and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q, assuming no air resistance?

Accepted Answer

We can solve this problem using kinematic equations. At point P, the vertical component of velocity is zero because the projectile has reached maximum height. We can use the vertical motion equation:

final velocity squared = initial velocity squared + 2acceleration(change in height)

At point P, final velocity is zero, initial velocity is 96 m/s, acceleration is -9.8 m/s^2 (negative because it is against the direction of motion), and the change in height is the height of point P above the ground (let's call it h). Plugging in these values, we get:

0 = (96)^2 + 2(-9.8)h
h = (96)^2/(2(9.8)) = 460.12 m

So, point P is 460.12 m above the ground. To find the height of point Q, we can use the horizontal motion equation:

distance = velocity x time

The horizontal velocity is constant, so we can use the time it takes for the projectile to reach the ground. We can find this time using the vertical motion equation:

final vertical velocity = initial vertical velocity + acceleration x time

At point Q, final velocity is -96 m/s (negative because it is in the opposite direction of initial velocity), initial velocity is also -96 m/s, acceleration is -9.8 m/s^2, and we want to solve for time. Plugging in these values, we get:

-96 = -96 - 9.8t
t = 9.8 seconds

Now, we can use the horizontal motion equation to find the distance traveled in 9.8 seconds:

distance = 940 m/s x 9.8 s = 9212 m

Therefore, point Q is 9212 m away from the edge of the cliff. The height of point P above Q is:

h = 460.12 m + 0 m - 9212 m = -8751.88 m

This negative value means that point P is below point Q, but we only care about the magnitude of the height difference, so the answer is:

B) 490 m

Question 15

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag.
(a) How fast was it thrown?
(b) How far from its original position did it land?
(c) How high above its original position did it go?

Accepted Answer

The answer of A projectile is thrown upward at 24°...

Question 16

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is

Accepted Answer

Since we are neglecting air resistance, the only force acting on the ball is gravity which points vertically downwards with magnitude 9.8 m/s^2. The initial velocity of the ball has a horizontal component (20*cos(25)) and a vertical component (20*sin(25)). The horizontal velocity is constant (since there is no force acting on it), while the vertical velocity changes due to the force of gravity. Therefore, the magnitude of the acceleration of the ball while it is in flight is equal to the magnitude of the gravitational acceleration, which is 9.8 m/s^2.

Question 17

You are driving at $30.0 \mathrm {~m} / \mathrm { s }$ on a freeway curve of radius $25.0 \mathrm {~m}$ What is the magnitude of your acceleration?

Accepted Answer

Centripetal acceleration is given by:$$a_c = \frac{v^2}{r} = \frac{(30.0 \mathrm {~m} / \mathrm { s })^2}{25.0 \mathrm {~m}} = 36.0 \mathrm {~m} / \mathrm { s }^2$$

Question 18

The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m?

Accepted Answer

The answer of The maximum acceleration a pilot can stand...

Question 19

As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of $v 0 x = 30 \mathrm {~m} / \mathrm { s }$ and $v 0 y = 300 \mathrm {~m} / \mathrm { s }$ The projectile rises and then falls into the sea at point P. The time of flight of the projectile is $75.0 \mathrm {~s} ,$ and air resistance is negligible. At this location, g = 9.80 m/s². What is the horizontal distance D?

Accepted Answer

The answer of As shown in the figure, a projectile...

Question 20

At a location where g = 9.80 m/s², a projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed?

Accepted Answer

The answer of At a location where g = 9.80...

Quiz 3: Vectors and Motion in Two Dimensions