The Trajectory of Spot:
Back to the main page/Back to the previous page

In Dick's frame

while in Jane's frame

Here v is Dick's (x-direction) velocity with respect to Jane, v_0y'  is the upward velocity given to Spot by Dick, and g is taken to be negative, since gravity pulls downward and Spot was thrown upward. Converting to Jane's frame (solving for the unprimed values),

Using these in the equation for y' provides

This is the equation for a parabola in x and y. If, for example, Dick moves relative to Jane at 5 m/s and he throws Spot upward at 10 m/s, then the equation of Spot's motion would be (I used g = 10 rather than 9.8 to make the calculation easier)

When plotted the result looks like this: