H(t) = vt -5 times (t) squared Factor H(t) and hence find the time when the ball falls back to the ground. Express this time in terms of v.

Question

thank you

Answer 1

H(t)=t(v-5t)=0 when the ball is on the ground, that is, when t=0 or t=v/5. When t=0 we have the initial condition, and when t=v/5 the ball has fallen back to the ground. Note that the vertex (maximum height) occurs at half this time, v/10 (see the answer to your other question).