plz solve 5th question
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→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.
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.
anurag36:
thank u
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