Question

1. A person standing on the edge of a cliff, at some height above the ground below, throws one ball straight up with initial speed u and then throws another ball straight down with the same initial speed. Which ball, if either, has the larger speed when it hits the ground? Neglect air resistance.

2. When a skydiver jumps out of a plane there are two forces acting on him a constant force due to gravity and varying force due to air resistance. His acceleration is given by a = g bv² where g is the acceleration due to gravity, v is his velocity and b is a constant (the co-efficient of drag). When he jumps from the plane he falls some thousands of feet before opening his parachute.

a.

b. What happens to the value of b when he opens his parachute?

c. Draw a sketch of the skydivers velocity as a function of time.

d. Draw a sketch of the skydivers acceleration as a function of time.

Answer 1

1. For the ball being thrown up.
$$\begin{gathered} v^2-u^2=2as \\ =0-u^2=-2gs \\ s=u^2/2g \\ Theballdescendsfromthisheightabovetheedgeofthecliff. \\ {u}^2/2g+hbethetotaldis\tan cetothebottom. \\ {v}^2-u^2=2as \\ v=\sqrt{2g(u^2/2g+h)} \\ =\sqrt{u^2+2gh)} \\ 2.Thesecondball. \\ {v}^2-u^2=2as \\ v=\sqrt{u^2+2gh)} \\ Bothhavethesamevelocitywhenthehittheground. \\ 2.a)Thevalueofbisacons\tan thencewouldremaincons\tan tevenafteropeningofthe \\ parachute. \\ b)Letsseehowthefunctionwouldbe. \\ Assuminghejustdroppedoutoftheplane, \\ dv=gn{v}^{2}dt \\ =\frac{dv}{gn{v}^2}=dt \\ =\frac{v^{-3}}{gn}=t=>t{v}^3=gn \end{gathered}$$