A tennis ball of mass 51.0 g is held just above a basketball of mass 596 g. With

Question

A tennis ball of mass 51.0 g is held just above a basketball of mass 596 g. With their centers vertically aligned, both are released from rest at the same moment, to fall through a distance of 1.06 m, as shown in the figure below.

Image --> http://www.webassign.net/serpse/p9-20.gif

(a) Find the magnitude of the downward velocity with which the basketball reaches the ground. Assume an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down.
m/s

(b) Next, the two balls meet in an elastic collision. To what height does the tennis ball rebound?
m

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) You now have 2 equations in 2 unknowns, v1 and v2. Plug in the values of the known mases, find the initial velocity v0 and plug itin, and solve the equatiolns for v1 and v2. Get v0 from the formula for velocity of body that falls a distance h: v = (2 g h )^1/2, (Eqn 3) where g = 9.80 m/s^2, and h = 1.10 m. So v0 = 4.64 m/s. The answer to a) is v0 = 4.64 m/s Next 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 (Eqn 5) The answer to b) is h2 of Eqn 5.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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