Science:Math Exam Resources/Courses/MATH100/December 2016/Question 06 (b)/Solution 1

We are told that $h(1)-h(0)=5$. Hence ${\begin{aligned}h(1)-h(0)&=(s_{0}+v_{0}-5)-s_{0}=v_{0}-5=5.\end{aligned}}$ Thus $v_{0}=10$.

Since the object falls down when it gets to its maximum height, the question, in fact, asks about the time at which ${\frac {dh}{dt}}=0$ .

Then ${\frac {dh}{dt}}=v_{0}-10t=10-10t=0$. So when $t=1$ the object starts to fall back down.

The answer is therefore $\color {blue}1\,{\text{s}}$ .