A boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved 100 m. If the truck is moving horizontally along a straight line with a constant speed 30 m/s, at what speed (relative to the truck) must the projectile is thrown. (Assume, `g = 10 m//s^2` )

Options

A. `55/3 m//s`
B. `43/2 m//s`
C. `50/3 m//s`
D. `23/2 m//s`

Answer

C, D

Explanation

Given,
Truck moves by 100 m
Velocity of truck = 30 m/s
`g =10 m//s ^(2)`
Time taken by truck to move 100 m
`g = (100)/(30) = (10)/(3) s`
Time taken by projectile `(t _(1))` to reach maximum height is given by,
`O = V_(1) - g t _(1)`
`V _(1) = g t _(1)`
Where, `V -` Projectile velocity in upward direaction.
But `t _(1) = 1/2`
`implies V_(1)=g xx (t_(1))/(2)`
` = 10 xx (10)/((3)/(2))`
`therefore V _(1) = (100)/(6) = (50)/(3) m//s `