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The horizontal and vertical displacement...

The horizontal and vertical displacements x and y of a projectile at a given time t are given by `x= 6 "t" and y= 8t -5t^2` meter.The range of the projectile in metre is:

A

`sin^(-1)(4/5)`

B

`sin^(-1)(3/5)`

C

`sin^(-1)(4/3)`

D

`sin^(-1)(3/4)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x = 36 t` and `2y = 96t - 9.8 t^(2)`
`v_(x) =(dx)/(dt) = 36` and `(dy)/(dt) = 48 - 9.8 t`
`t =0, u_(x) = 36` and `u_(y) = 48`
`tan theta = u_(y)/u_(x) = 48/36 = 4/3`
`sin theta 4/5 rArr theta = sin^(-1) (4/5)`
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