TPrj45

A golf ball traveling at 3.0 m/s rolls off a roof inclined at 37° from the horizontal with lower edge 30 m above the ground. A car is parked near the building with roof 1.0 m above the ground and 3.6 m from the edge of the building. Does the golf ball strike the car?

Draw a diagram of the problem with the edge of the roof located at the origin.

Set the coordinate system at the edge of the roof and look at the velocities.

The 3.0 m/s initial velocity at 37° has components in the horizontal and vertical directions. Take the coordinate system as positive x down and positive y to the right and write the equations.

The problem question translated into an algebra equation becomes:

“What is the value of y when x is 29 m?”

First, find the time for this.

Now y at this time

The golf ball lands beyond the car. Note that the algebra logic could have been “what x value corresponds to y = 3.6 m”. Also, x could have been written in terms of y and ask “What is y when x = 29?” or “What is x when y is 3.6?”.