Question

A cart is moving horizontally along a straight line with constant speed $30m/s.$ A particle is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was projected after the cart has moved $80m$. At what speed (relative to the cart in $m/s$) must the projectile be fired? (g= $10m/s^2$).

• A. $10$
• B. $10\sqrt{8}$
• C. $\frac{40}{3}$
• D. None of these

Answer 1

The correct option is C $\frac{40}{3}$

From the inertial frame this is a projectile motion with range 80m and horizontal velocity 30 m. Time of flight is 80/30=8/3 s. displacement along y direction is zero.
$H=ut-\frac{1}{2}g{t}^2=0\Rightarrow u=\frac{gt}{2}=\frac{10\times \frac{8}{3}}{2}=\frac{40}{3}m/s$