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?
A) 470 m
B) 490 m
C) 45,000 m
D) 940 m
E) 90,000 m

Question

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? 
A) 470 m 
B) 490 m 
C) 45,000 m 
D) 940 m 
E) 90,000 m

Quizplus · 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

A Projectile Is Fired from the Edge of a Cliff