Ball A has a mass of 3 kg and is moving with a velocity (v_a)_1 = 7 m/s when it

Question

Ball A has a mass of 3 kg and is moving with a velocity (v_a)_1 = 7 m/s when it makes a direct collision with ball B,  which has a mass of 2 5 kg and is moving with a velocity of (v_B)_1 = 5 m/s Suppose that e = 0 8 Neglect the size of the balls (Figure 1) Part A Determine the velocity of A just after the collision measured to the right Express your answer to three significant figures and include the the velocity is directed to the right and negative value if the velocity (v_A)_2 = _______ Part B Determine the velocity of B just after the collision measured to the right. Express your answer to three significant figures and include the the velocity is directed to the right and negative value if the velocity is (v_B)_2 = _______

Explanation / Answer

ma = 3 kg

Vai = velocity before collision for ball A = 7 m/s

Vaf = velocity after collision for ball A

mb = 2.5 kg

Vbi = velocity before collision for ball B = - 5 m/s

Vbf = velocity after collision for ball B

using conservation of momentum

ma Vai + mb Vbi = ma Vaf + mb Vbf

3 x 7 + 2.5 (-5) = 3 Vaf + 2.5 Vbf

3 Vaf + 2.5 Vbf = 8.5

Vbf = (8.5 - 3 Vaf )/2.5                          eq-1

using the formula

e = (Vbf - Vaf)/(Vai - Vbi)

0.8 (7 - (-5)) = Vbf - Vaf

using eq-1

9.6 = ((8.5 - 3 Vaf )/2.5) - Vaf

Vaf = - 2.82 m/s

using eq-1

Vbf = (8.5 - 3 (-2.82) )/2.5 = 6.8 m/s

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