Question

The tee of the world’s longest par 3 sits atop South Africa’s Hanglip Mountain at 400.0 m above the green. If a golfer launches a shot at 40° with the horizontal, what initial velocity must she give the ball?

a) 78.2 m/s
b) 84.5 m/s
c) 92.3 m/s
d) 101.8 m/s

Answer 1

To find the initial velocity of the golf ball launched from the tee atop Hanglip Mountain, we can use the principles of projectile motion. By splitting the initial velocity into horizontal and vertical components, and using the equations for distance and time of flight, we can solve for the initial velocity. The answer is approximately 84.5 m/s.

Step-by-step explanation:

To find the initial velocity of the golf ball, we can apply the principles of projectile motion. The horizontal distance to the green is 359.0 m and the height of the tee above the green is 400.0 m. We can use the horizontal distance to split the initial velocity into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component experiences acceleration due to gravity. Using trigonometry, we can find the initial velocity:

Initial velocity (V0) = Horizontal component of velocity (Vx) / Cos(θ)

Horizontal component of velocity (Vx) = Initial velocity (V0) * Cos(θ)

Height of the tee above the green (h) = Vertical component of velocity (Vy) * Time of flight (t) + (1/2) * Acceleration due to gravity (g) * Time of flight (t)^2

Replacing Vy with Initial velocity (V0) * Sin(θ) and rearranging the equation, we get:

h = V0 * Sin(θ) * t + (1/2) * g * t^2

Solving these equations simultaneously, we can find the initial velocity of the golf ball to be approximately 84.5 m/s.