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A projectile is thorwn with a velocity o...

A projectile is thorwn with a velocity of `50ms^(-1)` at an angle of `53^(@)` with the horizontal
Detemrine the instants at which the projectile is at the same height

A

`t = 1s` and `t = 7s`

B

`t = 3s` and `t = 5s`

C

`t = 2s` and `t = 6s`

D

all the above

Text Solution

Verified by Experts

The correct Answer is:
D
For same height
`y = u_(y)t +(1)/(2) a_(y)t^(2) rArr y = u_(y)t - (1)/(2) "gt"^(2)`
`"gt"^(2) - 2u_(y) +2h = 0 rArr t = (2u_(y)+-sqrt(4u_(y)^(2)-8gh))/(2g)`
`t_(1) = `(u_(y)-sqrt(u_(y)^(2)-2gh))/(g), t_(2) =(u_(y)-sqrt(u_(y)^(2)-2gh))/(g)`
`t_(1) +t_(2) =(2u_(y))/(g) = (2 xx 50 xx sin 53^(@))/(10) = 8sec`.
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