Question

plz solve 5th question

Answer 1

→Initial velocity = u
Angle of projection = α (alpha)

→ Let 'v' denote the velocity at a general time 't'

Suppose motion occurs in X-Y plane. Then direction of 'g' is along -Y axis.

So, for initial velocity,
Horizontal component = u cos α
Vertical component = u sin α

→ Now, in a projectile motion, the gravitational force acts vertically downwards. That means, the Gravitational Force can affect only the vertical component.

So, in a projectile motion, the horizontal component of velocity will remain same.

→Let horizontal component of v be Vx.

So, Vx = u cos α

→Also, let vertical component of v be Vy.

In vertical direction, as gravity is acting, motion is uniformly accelerated. So, in vertical direction,

Vy = Uy + a t

So, Vy = u sin α - gt (as g is along -Y)


→ Now, we have been told to find the time when horizontal component becomes equal to vertical component.

So, Vx =Vy
So, u cos α = u sin α - gt
So, gt = u sin α - u cos α
So, gt = [u(sin α - cos α)]
So, t = (u/g) [ sin α - cos α ]

Thus, your answer is option C.