Answer to Question #971 in Mechanics | Relativity for Nate

Question

You throw a 0.345kg ball straigt up with an initial velocity of 13.5m/s

a. what is the momentum of the ball at the highest point of its path?
b. what is its momentum halfway up?
c. what is its kinetic energy halfway up?

Answer 1

a. At the highest point of the motion the velocity equals to zero, p = mv = m*0 = 0;b. From the equations of the motion S = v²/2g; S_1/2 = v²/4g = 4.56 m.
v²/4g = vt - gt²/2;
4.56 = 13.5t - 5t²;
t₁ = 0.4 s; t₂ = 2.3 s.
v(t=0.4) = v-gt = 13.5 - 0.4*10 = 9.5 m/s.
The momentum is p= 0.345* 9.5 = 3.3 kg* m/s;
The energy is E = mv²/2 = 0.345* 9.5² / 2 = 6.2 J