Akash, a punter in a football game kicks a ball from the goal line at 52.0° from the horizontal at 29.0 m/s.

a) What is the hang time of the punt?

b) How far down field does the ball land?

(a)

θ = angle from the goal line = 52.0 deg

v₀ = initial velocity of launch = 29 m/s

consider the motion of the ball along the vertical direction

Y = vertical displacement = 0 m

a = acceleration = - 9.8 m/s²

v' = initial velocity along the Y-direction = v₀ Sinθ = (29) Sin52 = 22.85 m/s

t = hang time

using the equation

Y = v' t + (0.5) a t²

0 = (22.85) t + (0.5) ( - 9.8) t²

t = 4.7 sec

b)

Consider the motion along horizontal direction

X = displacement along X-direction

t = time taken = 4.7 sec

v'' = initial velocity along the X-direction = v₀ Cosθ = (29) Cos52 = 17.85 m/s

displacement along the X-direction is given as

X = v'' t

X = (17.85) (4.7)

X = 83.89 m