Question

In the following three scenarios, I do not understand one thing: how do we know that the initial velocity of the y component (vy0) is zero?

scenario A : Small-plane pilots regularly compete in “message drop” competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. A plane 60 m above the ground is flying directly toward a target at 45 m/s

scenario B: Trained dolphins are capable of a vertical leap of 7.0 m straight up from the surface of the water—an impressive feat. Suppose you could train a dolphin to launch itself out of the water at this same speed but at an angle. What maximum horizontal range could the dolphin achieve?

scenario C: A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it drop the package?

Answer 1

The y-component of the initial velocity vector is zero only in scenarios A and C. The weight/package on either plane inherits a non-zero x-component that matches the plane's horizontal velocity, but with respect to the vertical direction the objects are at rest, and dropping them from a given height doesn't confer them an initial vertical velocity. On the other hand, if the object was thrown upward and allowed to fall, or shot downward by a cannon, then the initial vertical velocity would be non-zero.

In scenario B, the dolphin must have some non-zero y-component of velocity in order to launch itself out of the water, because otherwise it would stay at a fixed depth.