A tennis ball of mass m(t) is held just above a basketball of mass m(b), With th

Question

A tennis ball of mass m(t) is held just above a basketball of mass m(b), With their centers vertically aligned, both are released from rest at the same moment, so that the bottom of the basketball falls freely through a height h and strikes the floor. Assume an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down because the balls have separated a bit while falling.

(a) The two balls meet in an elastic collision. To what height does the tennis ball rebound? (Use any variable or symbol stated above along with the following as necessary: g.)

Explanation / Answer

Conservation of momentum: m1 v0 - m2 v0 = m1 v1 + m2 v2 (Eqn 1) Conservation of kinetic energy: The coefficient (1/2) is factored out. m1 (v0)^2 + m2 (v0)^2 = m1 (v1)^2 + m2 (v2)^2 (Eqn 2) find height of bounce of ball 2 (tennis ball). For this you need the after-collision velocity of ball 2. Get this from equations 1 and 2. Rearrange Eqn 1 to get v1 = [ v0 (m1 - m2) - m2v2 ] / m1 (Eqn 4) Plug Eqn 4 into Eqn 2, rearrange to solve for v2. All the kinetic energy of ball 2 will be converted to gravitational potential energy as the ball rises to height h2. Rearrange Eqn 3 to get h2 = v2^2 / 2g (answer)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.