Two projectiles are launched from ground level at the same angle above the horizontal, and both return to ground level. Projectile A has a launch speed that is twice that of projectile B. (Sketch trajectories of projectiles). Assuming that air resistance is absent, what should the ratio of the maximum heights be and what should the ratio of the ranges be? Justify answer.

Question

Two projectiles are launched from ground level at the same angle above the horizontal, and both return to ground level.  Projectile A has a launch speed that is twice that of projectile B.  (Sketch trajectories of projectiles).  Assuming that air resistance is absent, what should the ratio of the maximum heights be and what should the ratio of the ranges be?  Justify answer.

drwls · Answer

The equation for maximum height is
H = (V^2/2g)* sin^2 A

The equation for range is
R = (V^2/g)*sin(2A)

where A is the launch angle, measured from horizontal.

Note that both are proportional to V^2.
Deriving the formulas would be a useful exercise for you.

Both trajectory curves will be upside down parabolas. They start out coinciding, and passing through the origin, but the one that goes 4 times higher also goes 4 times farther.