Question

A golf ball which is hit from a tee with a height of 2 inches (1/6 foot) at an angle of 37 degrees with initial velocity 55 feet / s.

a) Find a set of two parametric equations which model the path of the ball.

b) How far did the ball travel before it hit the ground?

Answer 1

h = 2 inches, angle = 37 degrees, initial velocity = 55 feet/s = 55*12 = 660 inches/s, g = 9.81 ms^-2 = 39.37*9.81 inches/s^2 = 386.22 inches/s^2

Part a

initial velocity in x-direction = 660*cos(37 deg) = 527.099 inches/s

initial velocity in y-direction = 660*sin(37 deg) = 397.198 inches/s

At any time t, horizontal position of the ball will be: X = 527.099*t

and,

vertical position of the ball will be Y = 397.198*t - (1/2)*386.22*t^2 = 397.198*t - 193.11*t^2

Part b

Time of flight T = (2*660*sin(37 deg))/386.22 = 2.057 seconds

The ball travels a distance of 527.099*2.057 = 1084.24 inches