Answer:
a) The final velocity is 20 m/s when the large-mass object is the one moving initially.
b) The final velocity is 9.0 m/s when the small-mass object is the one moving initially.
Explanation:
The momentum of the system is calculated as the sum of the momenta of each object. Each momentum is calculated as follows:
p = m · v
Where:
p = momentum.
m = mass.
v = velocity.
Then, the momentum of the system is the following:
m1 · v1 + m2 · v2 = (m1 + m2) · v
Where:
m1 = mass of the bigger object.
v1 = velocity of the bigger object.
m2 = mass of the smaller object.
v2 = velocity of the smaller object.
v = final velocity of the two objects after the collision.
Solving the equation for the final velocity:
(m1 · v1 + m2 · v2)/ (m1 + m2) = v
a) Let´s calculate the final velocity when the bigger object is moving:
(7.1 kg · 29 m/s + 3.2 kg · 0)/(7.1 kg + 3.2 kg) = v
<u>v = 20 m/s</u>
b) When the smaller object is moving:
(7.1 kg · 0 m/s + 3.2 kg · 29 m/s) / (7.1 kg + 3.2 kg) = v
<u>v = 9.0 m/s</u>
