Question

The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger’s frame of reference. Draw its path as viewed by a stationary observer.

Short answer

The path of the hat with respect to the jogger is a horizontal straight path, and the path of the hat for a stationary observer is the parabolic path.

Step-by-step solution

Frame of reference

A frame of reference is a collection of coordinates used to indicate the relationship between a moving observer and an event. The frame of reference is further classified into the inertial and the non-inertial frames of reference.

Explaining motion of hat with respect to jogger

The motion of the hat in the jogger’s frame of reference is represented as

The motion of the hat in the jogger’s frame of reference

In the frame of reference of the jogger, the hat falls in a straight path downwards.

Hence, the motion of the hat in the jogger’s frame of reference appears to fall on a horizontal path.

Explaining motion of hat with respect to stationary observer

The motion of the hat in the stationary observer’s frame of reference is represented as,

The motion of the hat in the stationary observer’s frame of reference

As the hat falls, the vertical component of the velocity increases due to the influence of acceleration due to gravity. So, the path will be parabolic with respect to a stationary observer.

Hence, the path of the hat for a stationary observer is the parabolic path.