Two shells are fired from a canon with seped (u) each, at angles if ` alpha` and ` beta` respectively with the horizontal . The time intrval between the shots is (t). They collide in mid air after time (T) from the first shot . Which of the following consitions must be satisfied ?

Options

A. ` alpha gt beta`
B. ` T cos alpha = (T- t) cos beta`
C. ` T- t) cos alpha = T cos beta`
D. ` usin alpha T - 1/2 g T^2 = u sin bwta (T- t) - 1/2 g (T- t)^2`

Answer

A, B, D

Explanation

Since the first shot must have travelled for more time than the second shot before collinding in mid air. It will be so if the angle of projection of first short ` alpha` is greater than the angle of projection of second shot ` beta i.e. alpha gt beta `.
At the colliding position of two shots , the borizontal distance (x) covereed by each shot is same so ` x= u cos alpha T = u cos beta (T - t)`
or ` T cos alpha = (T-t) cos beta`
At the colliding position of two shots, the vertical distance (y) covered by first shot is
` y= u sin alpha t - 1/2 g T^2`
The verrtical distance `y` covered by secnd shot is
` y = u sin beta (T- t) - 1/2 g (T -t)^2`
:. `u sin alpha T - 1/2 g T^2 = u sin beta (T-t) - 1/2 g (T-t)^2` .