Question

A 2.00-kg ball is moving at 2.20 m/s toward the right. It collides elastically with a 4.00-kg ball that is initially at rest. 1) Calculate the final velocity of the 2.00-kg ball. (Express your answer to three significant figures.)

Answer 1

The final velocity of the 2.00-kg ball after an elastic collision with a 4.00-kg ball at rest can be calculated by using the conservation of momentum and kinetic energy equations.

Step-by-step explanation:

To calculate the final velocity of the 2.00-kg ball after an elastic collision with a 4.00-kg ball, we can use the conservation of momentum and conservation of kinetic energy because elastic collisions conserve both momentum and kinetic energy. The initial momentum (pi) is the sum of the individual momenta of the two balls before the collision, and the final momentum (pf) is the sum after the collision.

The conservation of momentum can be expressed as:

m1v1i + m2v2i = m1v1f + m2v2f

For an elastic collision, the conservation of kinetic energy is also applicable:

0.5m1v1i2 + 0.5m2v2i2 = 0.5m1v1f2 + 0.5m2v2f2

Given:

• m1 = 2.00 kg (mass of the first ball)
• v1i = 2.20 m/s (initial velocity of the first ball)
• m2 = 4.00 kg (mass of the second ball at rest)
• v2i = 0 m/s (initial velocity of the second ball)

Since the second ball is at rest, its initial momentum and kinetic energy are zero. After plugging in the values and solving the system of equations formed by the conservation laws, the final velocity of the 2.00-kg ball (v1f) can be found.

Answer 2

Elastic collision is when kinetic energy before = kinetic energy after

Ek= 1/2mv^2

total before
Ek=1/2(2)(2.2^2) = 4.84 J

total after
Ek= 1/2(2+4)(v^2) = 3v^2

Before = after
4.84=3v^2 | divide by 3
121/75 = v^2 | square root both sides
v=1.27 m/s