A particle at a height h from the ground is projected with an angle 30 ° from the horizontal. It strikes the ground making an angle 45 ° with the horizontal. It is again projected from the same point with the same speed, but with an angle of 60 ° with the horizontal. Find the angle it makes with the horizontal when it strikes the ground.

Step-by-step solution

In a projectile, the horizontal component of velocity remains constant. v x = u x = u   cos 30 ° = 3 2 u Here, x and y are the components of velocity at the time it strikes the surface must be equal, because it strikes the surface at an angle of 45 ° . ∴ v y = 3 2 u So, v = v x 2 + v y 2 = 3 2 u We know that, v is independent of the angle of projection. So, the velocity with which it strikes the surface for the second case remains v = 3 2 u . Let, it strike at angle ϕ , then, v cos ϕ