Question

A ball is shot vertically upwards from the surface of a planet in a distant solar system. A plot of the $y$ versus $t$ for the ball is shown in fig. The magnitude of the free fall in $m/s^2$ on the planet is

• A. $8$
• B. $12$
• C. $16$
• D. $4$

Answer 1

The correct option is A $8$

From graph, the ball takes $2.5s$ to reach $y_{max}$

and $2.5$ to get back down

From the top of its movement

Where $v_{top}=0$

$y_{max}=v_{top}{v}_{down}+\frac{1}{2}a{t}_{down}^2$

$y_{max}=\frac{1}{2}a{t}_{down}^2$

$\therefore a=\frac{2y_{max}}{t^2}$

$\therefore a=\frac{2\times 25}{{\left(2.5\right)}^2}$

$a=8$