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Two shells are fired from a cannot with ...

Two shells are fired from a cannot with a speed u each, at angles of `alpha` and `beta` respectively to the horizontal. The time interval between the shots is T. they collide in mid-air after time t from the first shot. Which of the following conditions must be satisfied ?

A

`aplha gt beta`

B

`t cos alpha=(t-T)cos beta`

C

`(t-T)cos alpha=t cos beta`

D

`(usinalpha)t-1/2"gt"^2=(usinbeta)(t-T)-1/2g(t-T)^2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
1st shell, `x=u cos alpha t, y=u sin alpha t-(gt^(2))/(2)`
For 2nd shell, `x=u cos beta(t-T)`
`y=u sin beta(t-T)-g ((t-T)^(2))/(2) rArr t cos alpha =(t-T) cos beta as t gt t-T rArr cos alpha lt cos beta rArr alpha gt beta" Equating y" rArr u sin alpha t-1/2 gt^(2) =u sin beta (t-T)-1/2 g(t-T)^(2)`
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