Question

A projectile is thrown with a velocity of `10 ms^(-1)` at an angle of `60^(@)` with horizontal. The interval between the moments when speed is `sqrt(5g) m//s` is (Take, `g = 10 ms^(-2))`
A. 1s
B. 3s
C. 2s
D. 4s

Answer 1

Correct Answer - C
`v^(2) = v_(y)^(2) +v_(x)^(2)` or `5g = (u_(y) - g t)^(2) +u_(x)^(2)`
Since, `v_(y) = u sin 30^(@) = 10 sin 30^(@) = 5sqrt(3) ms^(-1)`
`v_(x) = u cos 30^(@) = 10 cos 30^(@) = 5 ms^(-1)`
or `50 = (5sqrt(3) - 10t)^(2) +(5)^(2)`
`:. (5sqrt(3) -10t) = +- 5`
`t_(1) = (5sqrt(3)+15)/(10)` and `t_(2) = (5sqrt(3)-5)/(10)`
`:. t_(1) - t_(2) = 2s`