A cart is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 120m. At what speed (relative to the cart, in m/s) must the projectile be fired ? (Take `g=10m//s^2`)

Answer

25

Explanation

Time taken by the cart to cover 120m, `t=s/v, (120m)/(30m//s)=4s`
For the projectile to return to cart, it must be fired vertically upwards relative to cart. Considering the vertical motion of projectile from point of projection to highest point of its trajectory `v_(y)=u_(y)+a_(y)t, v_(y)=0, u_(y)=? a_(y)=-g=-10m//s^(2), t=4/2 =2s,`
`0=u_(y)-10 xx 2 rArr u_(y)=20m//s`