# 2.3.2 Vertical throw

If a mass is thrown upward, it rises, then falls back down. This motion’s v-t and s-t graphs (↑+ve sign convention) will look like

• v-t graph is a straight line graph with gradient corresponding to downward 9.81 m s-2, both on the way up and down. The triangular area corresponds to the maximum height reached.
• s-t graph is a quadratic curve, with initial gradient equal to u.

Example

A frog jumps vertically.

a) At what speed must the frog lift off the ground if it were to rise through a height of 50 cm?

b) For how long does the frog stay in the air?

Solution

a)

Since $v=0$ at maximum height, \begin{aligned}({{v}^{2}}&={{u}^{2}}+2as)\\0&={{u}^{2}}+2(-9.81)(0.50)\\u&=3.132=3.13\text{ m }{{\text{s}}^{{-1}}}\end{aligned}

b)

Time to reach the peak tp $\displaystyle =\frac{{\Delta v}}{a}=\frac{{3.132}}{{9.81}}=0.3193\text{ s}$

It takes equal amount of time to go up as come down.

So the total time it stays in the air $=2\times {{t}_{p}}=2\times 0.3193=0.639\text{ s}$

Video Explanation

Vertical Throw

Demonstration

One-Hand-Juggler