A golf ball is hit from ground level on a horizontal fairway with initial veloci

Question

A golf ball is hit from ground level on a horizontal fairway with initial velocity vector v0 = v0xi + v0yj. Throughout its trajectory, the golf ball encounters a strong wind which causes the ball to experience an acceleration in the horizontal direction with a magnitude of 1.05 m/s2
as shown in the figure. Assume that any other air resistance is negligible. Use a Cartesian coordinate system with the origin at the ball's initial position as shown in the figure.

Randomized Variables

a) Calculate the max height, hmax in meters, that the ball achieves.

b) How long ttotal in seconds, is the ball in the air before it returns to the ground?

c) Describe the ball’s horizontal position as a function of time, x(t), (in terms of v0x, v0y, awind, and g) before it returns to the fairway.

d) Describe the ball’s horizontal position as a function of time, x(t), (in terms of v0x, v0y, awind, and g) before it returns to the fairway.

Explanation / Answer

What do you want to derive here ?
v0 = v0xi + v0yj.

v0 = 14i + 7.5j

Vertical velocity at time t can be defined as :

v(t) = v0 - 9.8*t

v(t) = 7.5 - 9.8*t

At the top the veritcal velocity will be zero hence

t = 7.5/9.8

t = 0.765 sec.

Hence the total time of travel of the ball is 0.765*2 = 1.53 sec

Horizontal velocity can be defined at time t as :

v(t) = 14 - 1.05*t

Hence the total distance travelled by the ball in the time 1.53 sec is :

s = ut + 1/2at^2

s = 14*1.53 - 0.5*1.05*1.53^2

s = 20.19 m

The velocity at any time t of the ball can be defined as

v = ( 14 - 1.05*t )i +  (7.5 - 9.8*t) j

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