Question

A train is moving along a straight line with a constant acceleration $a$. A boy standing in the train throws a ball forward with a speed of $10m/s$, with respect to the train at an angle of ${60}^0$ to the horizontal. The boy has to move forward by $1.15m$ inside the train to catch the ball back at the initial height. The acceleration of the train, in $m/s^2$, is:

• A. 5
• B. 4
• C. 6
• D. 1

Answer 1

The correct option is A 5

Ball performs parabolic motion,
For vertical motion,
$s=ut-\frac{1}{2}g{t}^2$
$\therefore 0=10sin{60}^{o}t-\frac{1}{2}\times 10\times t^2$
$\therefore t=\sqrt{3}s$
For horizontal motion,
$s=ut+\frac{1}{2}a{t}^2$
$\therefore 1.15=10cos{60}^o\times \sqrt{3}-\frac{1}{2}a\left(3\right)$
$\therefore a=5m/s^2$