A cart is moving horizontally along a straight line with constant speed `30 ms^-1.` 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 `80 m.` At what speed (relative to the cart) must the projectile be fired? (Take `g = 10 ms^-2`)

Options

A. `10 ms^(-1)`
B. `(20)/(3)ms^(-1)`
C. `(40)/(3)ms^(-1)`
D. `(80)/(3)ms^(-1)`

Answer

C

Explanation

The time taken by cart to cover 80 m
`(s)/(v) = (80)/(30) = (8)/(3)s`
The projectile must be fired (relative to cart) vertically upwards.
`a =- g =- 10 ms^(-2), v' = 0` and `t = (8//3)/(2) = (4)/(3)s`
`:. V' = u +at` or `0 = u - 10 xx (4)/(3)` or `u = (40)/(3) ms^(-1)`