A stone is thrown straight up from the edge of a roof, 1000 feet above the ground, at a speed of 14 feet per second. What is the velocity of the stone when it hits the ground?
The equation for displacement is `s(t)=-16t^2+v_0t+s_0` where `v_0` isthe initial velocity and `s_0` is the initial displacement. We adopt the convention that velocity towards the earth is negative:
So we have `s(t)=-16t^2+14t+1000` The velocity function is the first derivative of the displacement function with respect to t:
Solving for when the stone hits the ground we get:
`t=(-14+-sqrt(14^2-4(-16)(1000)))/(-32)` ==>`t~~-7.48,t~~8.355` seconds.
So with `t~~8.355` seconds, we find the velocity to be :
The velocity is approximately 253.4 feet per second towards the ground.