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Suppose two particles 1 and 2 are projec...

Suppose two particles `1 and 2` are projected in vertical plane simultaneously.
Their angles of projection are `30^@ and theta`, respectively, with the horizontal. Let they collide after a time`t` in air. Then
.

A

`theta = sin^-1(4//5)` and they will have same speed just before the collision.

B

`theta = sin^-1(4//5)` and they will have different speed just before the collision.

C

`x lt 1280 sqrt(3) - 960 m`.

D

It is possible that the particles collide when both of them are at their highest point.

Text Solution

Verified by Experts

The correct Answer is:
C, D
(b.,c.,d.) If they collide, their vertical component of velocities should be same, i.e.,
`100 sin theta = 160 sin 30^@`
`rArr sin theta = 4//5`
Their vertical components will always be same. Horizontal components :
`160 cos 30 = 80 sqrt(3) ms^-1`
and `100 cos theta = 100 xx 3//5 = 60 ms^-1`
They are not same, hence their velocities will not be same at any time. So (b) is correct.
`x = x_1 - x_2 = 160 cos 30^@ t - 100 cos theta t`
`rArr x = (80 sqrt(3) - 60) t`
Time of flight : `T = (2 xx 160 xx sin 30)/(g) = 16 s` (same for both)
Now `t lt T_x rarr` to collide in air
`rArr (x)/(80 sqrt(3) - 60) lt16 rArr x lt 1280 sqrt(3) - 960`
Since their times of flight are same, they will simultaneously reach their maximum height. So it is possible to collide at the highest point for certain values of `x`.
.
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