Find the ball's speed of projection

Question

A golf ball is struck by a golf club from a point on flat, horizontal ground. It leaves the ground at an angle of 40° to the horizontal. 2 seconds after being struck, the ball is travelling upwards at an angle of 10° to the horizontal. Find the ball's speed of projection

Answer 1

v = initial speed

 

v_y(t) = v sin40° - gt = v sin40° - 9.8t

v_x = v cos40° = constant

 

At t = 2,

 

v_y/v_x = tan10° ⇒ v_y = v_xtan10° ⇒

 

v sin40° - 9.8(2) = v_xtan10° = (v cos40°)tan10°

 

v sin40° - 19.6 = v cos40° tan10°

 

v(0.6428) - 19.6 = v(0.1351)

 

Can you solve for v and finish from here? You will get m/s.