Question

Two particles are projected from the same point on level ground simu ltaneously with the same velocity u but at the angles `(alpha+beta)` and `(alpha-beta)` of projection `betalt45^(@)` respectively. Which of the following statements will be true?
A. They will have the same horizontal range if `alpha=45^(@)`
B. They will be separated by the distance of `(2u^(2))/(g)(sin 2alpha cos 2beta)` when they reach the ground
C. They are sever in the same horizontal level during their flights.
D. none of these

Answer 1

Correct Answer - a,b,c,d
For two angles `(45^(@)+theta)` and `(45^(@)+theta)` range is same.
Time for reaching the maximum heights
`t_(1)=(u sin (45^(@)+theta))/(g)` and `t_(2)=(u sin(45^(@)-theta))/(g)`
or `Deltat=(u)/(g)[sin(alpha+theta)-sin(alpha-theta)]`
Similarly, `R_(1)=(u^(2))/(g)sin 2(alpha+beta)`
and `R_(2)=(u^(2))/(g)sin 2(alpha-beta)`