Question

A) Find the time tH it takes the projectile to reach its maximum height H.

B) Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R.

C) Find H, the maximum height attained by the projectile.

D) Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Answer 1

(A) Time taken by the projectile to reach its maximum height which will be given as -

using equation of motion (1), we get

v_y = v_0,y + a t

0 = (v₀ sin ) - g t_H

g t_H = (v₀ sin )

t_H = (v₀ sin ) / g

(B) Time taken by the projectile to hits the ground after having traveled through a horizontal distance which will be given as -

we know that, t_R = 2 t_H

t_R = 2 (v₀ sin ) / g

(C) The maximum height attained by a projectile which will be given as -

using equation of motion (3), we get

v_y² = v_0,y² + 2 g H_max

(v₀ sin )² = (0)² + 2 g H_max

v₀² sin² = 2 g H_max

H_max = (v₀² sin²) / 2g

(D) The total distance traveled in x direction which will be given by -

R = v_0,x t_R

R = (v₀ cos ) [2 (v₀ sin ) / g]

R = 2 v₀² sin cos / g                                    

R = v₀² sin 2 / g