The Stuntman, the Skis and the Rocket Launcher
A fascinating problem in relative velocity
Imagine a stuntman gliding effortlessly on skis through a frictionless region. He is carrying a rocket launcher and moving horizontally at a speed of v m/s. Suddenly, he fires a rocket with a muzzle speed of 4v.
Here comes the interesting part: despite firing the rocket, the stuntman's velocity remains unchanged!
At what angle above the horizontal, measured relative to the ground, was the rocket launched? (Ignore air resistance.)
Understanding the physics
The key to solving this problem is to distinguish between the velocity of the rocket relative to the launcher and its velocity relative to the ground.
Since the stuntman's velocity remains unchanged after firing, there can be no horizontal recoil. This means the rocket must be fired vertically upward relative to the stuntman.
But remember, the stuntman himself is already moving horizontally at a speed of v m/s. Consequently, an observer standing on the ground sees the rocket moving both horizontally and vertically.
Let θ be the angle the rocket's velocity makes with the horizontal, as measured by an observer on the ground.
Using the right-angled velocity triangle,
A rocket fired vertically relative to a moving launcher does not travel vertically relative to the ground. Its actual direction depends on the motion of the launcher itself. A neat illustration of the fascinating idea of relative velocity!