Question

According to the Guinness World Records, the fastest golf drive was achieved by Maurice Allen (USA) at the Americas Golf Outlet in Orlando, Florida, on March 3rd 2012. It was a stunning v0 = 339.56 km/h (211 mi/h) = 94.322 m/s, and (we assume) it made an angle of θ0 = 45.0˚ with the horizontal. The aerodynamic lift on the golf ball (due to its fast spin and dented design) keeps the ball longer in the air, so please assume that this effect cancels the negative effects of air drag thus giving the golf ball the same path as a projectile in the absence of the atmosphere.

a. Determine the horizontal (x-component) component v0x of this initial velocity vector v0.    (The following may be useful:   sin45.0˚ = 0.707107, cos45.0˚ = 0.707107, tan45.0˚ = 1)

b. Determine the vertical (y-component) component v0y of this initial velocity vector v0.    (The following may be useful:   sin45.0˚ = 0.707107, cos45.0˚ = 0.707107, tan45.0˚ = 1)

c. How far above the ground H was the golf ball at the highest point of its trajectory?

d. Find the total time t that the golf ball stayed in the air.

e. What is vx, the x-component of the final velocity vector v?

f. Assuming the golf course to be completely flat, how far (Δx) from its launch site does the golfball strike the ground?

Answer 1

Part A

The horizontal component is given by

Part B

The vertical component is given by

Part C

The height can be calculated by considering the initial velocity of the balls its horizontal velocity, and the gravity as a retarding force.

Part D

The total time the ball stays in the air is double the time it takes to achieve its maximum height. In other words, it is double the time gravity takes to reduce its initial velocity to zero.

The time the ball is in the air is double this time

Part E

The X-component, or the horizontal component, does not unedergo any acceleration or deceleration. Therefore, it is the same as the initial X-component.

Part F

The total distance travelled by the ball is the air time(calculated in Part D) times the X-component of the velocity vector.