Answer to Question #137044 in Physics for Mat

Question

A screw was detached from a hot air balloon that is rising at 3.5 m/s at an altitude of 8.3 m. (a) What is the initial velocity of the screw? (b) How long will it take for the screw to reach the ground?

Answer 1

(a) the initial velocity of the screw is directed upright

$$v_i=3.5\:\rm m/s$$

(b) the equation of motion of the screw

$$y=8.3+3.5t-\frac{9.8t^2}{2}$$

When the screw reaches the ground $y=0,$ so

$$8.3+3.5t-4.9t^2=0$$

$$t=1.7\:\rm s$$