A golf ball is struck with a five iron on level ground. It lands 92.2 m away 4.30 s later. What were (a) the direction and (b) the magnitude of the initial velocity

Vi = 29.83 m/s,   θ = 54.7⁰

Explanation:

Given:

Horizontal Distance x= 92.2 m

Time t = 4.30s s

To find Initial Velocity Vi =?

we have x = V t

Vix= Horizontal Component and Viy is vertical Component

Vix = x / t = 92.2 m / 4.30 s = 21.11 m/s

from 2nd Eqn of motion

y = Viy t + 1/2 g t²    

0 = Viy × 4.3 + 0.5 × (-9.81) m/s² × (4.3)²

we get Vy = 21.09 m/s

Vi = Square root ( Vix ² + Viy²)

Vi = 29.83 m/s

For Direction

Tan θ = Viy / vix

⇒  θ = Tan ⁻¹ ( 29.83  / 21.11 )

θ = 54.7⁰