Answer to Question #113128 in Mechanics | Relativity for Pierre Carlo Belarmino

Question

A rubber ball was launched at a velocity of +5 m/s at an angle where its range is at a maximum. A target is located exactly 2.0 meters from where the ball was launched.

a) What is the velocity of the ball as soon as it hits the ground?

b) Will the rubber ball hit the target? If no, at what angle should the ball be launched for it to hit the target?

Answer 1

(a) The velocity of the ball as soon as it hits the ground

$$v=5\:\rm m/s$$

(b) The range

$$R_{\rm max}=\frac{v_0^2}{g}=\frac{5^2}{9.8}=2.5\:\rm m\neq2.0\:\rm m$$

Hence, the rubber ball doesn't hit the target.

$$R=\frac{v_0^2\sin2\theta}{g}=\frac{5^2\sin2\theta}{9.8}=2.0$$

$$\theta=26^{\circ}$$