Question

A projectile is fired with a speed u at an angle `theta` with the horizontal. Its speed when its direction of motion makes an angle `alpha` with the horizontal is?

A: `usecthetasecalpha`
B: `usecthetasinalpha`
C: `ucosthetasecalpha`
D: `usinthetasecalpha`
PLEASE EXPLAIN EACH AND EVERY STEP

Answer 1

Let the velocity of projection of the object be u with angle of projection `theta` with the horizontal direction.
The vertical component of the velocity of projection is `usintheta` and the horizontal component is `ucostheta`

Now if t be the time after the projection of the projectile, its direction of velocity makes angle `alpha` with the horizontal.Let the velocity of the projectile after t sec be `v`

The vertical component of the velocity after time `t` will be `vsinalpha`

But the horizontal component remains unaltered as `ucostheta`

So `vcosalpha=ucostheta`

`=>v=1/cosalphaxxucostheta=ucosthetasecalpha`

So option C is accepted