Question

A ball is shot vertically upward from the surface of another planet. A plot of 'y' versus 't' for the ball is shown in figure where y is the height of the ball above its starting point and t = 0 at the instant the ball is shot. The figure's vertical scaling is set by $y_s$ = 30.0 m. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?

• A. a = - 8 m/, u = + 20 m/s
• B. a = 8 m/, u = + 20 m/s
• C. a = - g m/, u = + 22.5 m/s
• D. a = - 10/, u = + 25 m/s

Answer 1

The correct option is A

a = - 8 m/, u = + 20 m/s

Given $y_s$= 30. From graph maximum height = 25 m

Total time of flights of ball = 5 sec

Let the Ball be thrown with velocity u

When ball reaches the highest point velocity = 0

$\Rightarrow$ v = u + at

$\Rightarrow$0 = u - at , $t=\frac{u}{a}$

The ball will take same time to fall from that point

So the total time of flight = $\frac{2u}{a}$ = 5

$\frac{u}{a}=\frac{5}{2}$ $\Rightarrow u=\frac{5a}{2}$ .....(1)

Also $s=ut+\frac{1}{2}a{t}^2$

$2s-u\frac{5}{2}+\frac{1}{2}(-a)(\frac{5}{2}{)}^2$

Subtracting equation (1)

$25=\frac{25}{4}a-\frac{25}{4}a$

$25=\frac{25}{8}a$

a = 8 m/s² in down ward as we already assumed a to be downward and solved 80

a = - 8m/s²

u = 20 m/s