Question

Ethan throws a ball into the air from a cliff that is 152.4m high with an initial velocity of 4m/s. how long does it take for the ball to hit the ground.

Answer 1

First let's identify what we know. The initial height is 152.4 m, the final height is 0 m, the initial velocity is 4 m/s, acceleration is -9.8 m/s^2, and we are looking for the time in seconds.

Now let's choose a kinematic equation to use that has some of our knowns in it to solve for time:

yf - yi = vi*t + 0.5*a*t^2

Now plug in values:

0 - 152.4 = 4t + 0.5(-9.8)t^2

Simplify:

-4.9t^2 + 4t + 152.4 = 0

Solve using the quadratic formula:

t = -5.184 seconds or 6 seconds

We can eliminate -5.184 because that would mean the ball hit the ground before it was thrown.

The answer is 6 s.