Question

The velocity – time graph of a stone thrown vertically upward with an initial velocity of $30{\text{ms}}^{-1}$ is shown in the figure below. The velocity in the upward direction is taken as positive and that in downward direction as negative. What is the maximum height to which the stone rises?

• A. $30\text{m}$
• B. $45\text{m}$
• C. $60\text{m}$
• D. $90\text{m}$

Answer 1

The correct option is B $45\text{m}$

Given $u=30{\text{ms}}^{-1}$

From figure above, the acceleration $a$ = slope of line $AB$ $=\frac{-30{\text{ms}}^{-1}}{3\text{s}}=-10{\text{ms}}^{-2}$
The maximum height is reached when final velocity $v=0$. Using the value of $u,v$ and $a$ in relation
$v^2-u^2=2as$, we get
$0-{30}^2=2\times (-10)\times s$
or $s=\frac{30\times 30}{20}=45\text{m}$
Hence the correct choice is (b).