🤓 Based on our data, we think this question is relevant for Professor Efthimiou's class at UCF.
For this problem, we're looking for the launch height and final speed of the golf ball given the magnitude and direction of the initial velocity and the horizontal distance it has to travel.
For projectile motion problems in general, we'll follow these steps to solve:
The four UAM (kinematics) equations are:
In our coordinate system, the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because the only acceleration acting on a projectile once it's launched is gravity.)
For projectiles with a positive launch angle, we also need to know how to decompose a velocity vector into its x- and y-components:
And the equations to find the magnitude and direction of a velocity from the components:
A golfer tees off from the top of a rise, giving the golf ball an initial velocity of 43.0 m/s at an angle of 30.0° above the horizontal. The ball strikes the fairway a horizontal distance of 180 m from the tee. Assume the fairway is level. (a) How high is the rise above the fairway? (b) What is the speed of the ball as it strikes the fairway?