Question

1. A T-shirt cannon launches a shirt at 5.00 m/s from a platform height of 5.00 m from ground level. How fast will the shirt be traveling if it is caught by someone whose hands are (a) 2.00 m from ground level? (b) 3.00 m from ground level? Neglect air drag. 
2. Grains from a hopper falls at a rate of 30 kg/s vertically onto a conveyor belt that is moving horizontally at a constant speed of 5 m/s. (a) What force is needed to keep the conveyor belt moving at the constant velocity? (b) What is the minimum power of the motor driving the conveyor belt?

Answer 1

The law of conservation of energy says

$$\frac{mv_1^2}{2}+mgh_1=\frac{mv_2^2}{2}+mgh_2$$

$$v_2=\sqrt{v_1^2+2g(h_2-h_1)}$$

(a)

$$v_2=\sqrt{5^2+2*9.8(5-2)}=9.2\:\rm m/s$$

(b)

$$v_2=\sqrt{5^2+2*9.8(5-3)}=8.0\:\rm m/s$$