Ignoring air resistance. One athlete has a vertical “jump” of 20 inches. What is the initial velocity required to jump this high?

Question

Ignoring air resistance. One athlete has a vertical “jump” of 20 inches.  What is the initial velocity required to jump this high?

anonymous · Answer

@AnimalAin  can u help?

anonymous · Answer

Sure.  We know that $$s(t)=-16t^2+v_0t+s_0$$works for projectile motion without aero drag.  The ball player starts and ends on the floor, so s sub 0 = 0.  That means$$s(t)=-16t^2+v_0t$$

anonymous · Answer

We know the t value at maximum height is $$t_{\max s}=\frac{-b}{2a}=\frac{v_0}{32}$$and that 20 inches is 5/3 feet, which is the maximum height.

anonymous · Answer

So, by substitution,$$\frac{5}{3}=-16(\frac{v_0}{32})^2+v_0(\frac{v_0}{32})$$Can you solve that for v0 ?

anonymous · Answer

yes

anonymous · Answer

thx

anonymous · Answer

No sweat.  Do math every day.

anonymous · Answer

okay

anonymous · Answer

hmm i'm trying to solve but im getting it wrong

anonymous · Answer

OK, lets keep going here....  If we simplify the RHS of my equation above, we will get$$\frac{5}{3}=\frac{v_0^2}{64} \implies v_0=\frac{8\sqrt{15}}{3} \approx 10.3~fps$$

anonymous · Answer

Hope that was helpful.  Gotta go.  Do math every day.

anonymous · Answer

ok thx