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

Quizplus · Accepted Answer

First, we can find the time it takes for the projectile to reach its maximum height using the vertical component of its initial velocity. 
vf = vi + at 
0 = 96 + (-9.8)t 
t = 9.8 seconds

We can then find the maximum height using the vertical component of position at this time. 
y = vi*t + 1/2at^2 
y = 96(9.8) + 1/2(-9.8)(9.8)^2 
y = 470.4 meters

Finally, we can find the horizontal distance traveled by the projectile using the horizontal component of its initial velocity and the time it takes to fall to the ground, which is twice the time it took to reach the maximum height. 
x = vixt 
x = 940(2*9.8) 
x = 18,412 meters

Therefore, the height of point P above point Q is 470.4 meters.

A Projectile Is Fired from the Edge of a Cliff