Question

John and Kevin play catch with a
tennis ball while standing on skateboards. Initially John is moving
to the right at 6.50 m/s and Kevin is moving to the left at 4.00
m/s. John’s mass is 63.0 kg, Kevin’s mass is 70.0 kg, and the mass
of the tennis ball is 7.50 kg. John starts out with the tennis
ball, and throws it towards Kevin. The tennis ball moves towards
Kevin with ground speed 12.0 m/s.

(a) What is John’s speed immediately after throwing the tennis ball?

(b) What is Kevin’s speed immediately after catching the tennis ball?

Solve using momentum conservation

Answer #1

here,

mass of John , m1 = 63 kg

mass of tennis ball 2 , m2 = 7.5 kg

mass of Kevin m2 = 70 kg

a)

initial speed of john , u1 = 6.5 m/s

final speed of tennnis ball , v2 = 12 m/s

let the John’s speed immediately after throwing the tennis ball be v1

using conservation of momentum

(m1 + m2) * u1 = m1 * v1 + m2 * v2

( 63 + 7.5) * 6.5 = 63 * v1 + 7.5 * 12

solving for v1

v1 = 5.84 m/s

the final speed of john is 5.84 m/s to the right

b)

initial speed of Kevin , u3 = - 4 m/s

final speed of tennnis ball , v2 = 12 m/s

let the Kevin’s speed immediately after catching the tennis ball be v3

using conservation of momentum

(m3) * u3 + m2 * v2 = (m3 + m2) * v3

- 70 * 4 + 7.5 * 12 = ( 70 + 7.5) * v3

solving for v3

v3 = - 2.45 m/s

the final speed of john is 2.45 m/s to the left

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