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 80 m. At what speed (Relative to the cart) must the projectiie be fired? (Take g = 10 ms - 2 )

Question

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 80 m. At what speed (Relative to the cart) must the projectiie be fired? (Take g = 10 ms - 2 ) (A)  10 ms - 1  (B)  10 √ 8 ms - 1  (C)  ( 40 / 3 ) ms - 1  (D) None of these

Tardigrade Admin · Accepted Answer

As seen from the cart, the projectile the moves vertically upward and comes back. The time taken by cart to cover 80 m

\frac{s}{v} = \frac{80}{30} = \frac{8}{3} s

For a projectiie going upward
a = - g = - 10

m s^{- 2}

v = 0
and t =

\frac{8/3}{2} = \frac{4}{3} s

∴ v = u + a t

0 = u - 10

\times \frac{4}{3}

u =

\frac{40}{3} m / s

$10 m s^{- 1}$

$108 m s^{- 1}$

$\frac{40}{3} m s^{- 1}$

None of these

Q. 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 80 m. At what speed (Relative to the cart) must the projectiie be fired? (Take g = 10ms−2 )

10ms−1

108​ms−1

340​ms−1

None of these

As seen from the cart, the projectile the moves vertically upward and comes back. The time taken by cart to cover 80 m vs​=3080​=38​s For a projectiie going upward a = - g = - 10 ms−2 v = 0 and t = 28/3​=34​s ∴v=u+at 0 = u - 10 ×34​ u = 340​m/s

$10 m s^{- 1}$

$108 m s^{- 1}$

$\frac{40}{3} m s^{- 1}$