A particle is thrown such that its time of flight is `10 s` and horizontal range is `500 m`.
(i) `H_(max) = 125 m`
(ii) `u = 50 sqrt(2) m//s`
(iii) `theta = 45^(@)`
(iv) velocity at highest point `= 50 m//s`

Options

A. (i), (ii), (iii)
B. (ii), (iii), (iv)
C. (i), (ii), (iv)
D. all option are correct

Answer

D

Explanation

`T = (2u sin theta)/(g) = 10 rArr u sin theta = 50`
`R = u cos theta T rArr 500 = u cos theta xx 10 rArr u cos theta = 50`
(i) `H_(max) = (u^(2) sin^(2) theta)/(2g) = ((50)^(2))/(2 xx 10) = 125 m`
(ii) `u = sqrt((u sin theta)^(2) + (u cos theta)^(2)) = 50 sqrt(2) m//s`
(iii) `tan theta = (u sin theta)/(u sin theta) = 1 rArr theta = 45^(@)`
(iv) velocity at highest point `= u cos theta = 50 m//s`