an object of mass 3 kg is moving in the positive x-direction with a speed of 10 m/s. A second object of mass 5 kg is moving in the northwest direction with a speed of 8 m/s. If the two stick together after the collision, what is the final velocity
3.4
To find the final velocity of the two objects after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. In this case, we have two objects:
1. Object 1:
Mass (m1) = 3 kg
Initial velocity (v1) = 10 m/s
2. Object 2:
Mass (m2) = 5 kg
Initial velocity (v2) = 8 m/s
To calculate the total momentum before the collision, we add the individual momenta of the two objects:
Total momentum before the collision (p_initial) = (m1 * v1) + (m2 * v2)
Now, since the two objects stick together after the collision, they move as one combined object.
Let's assume the final velocity of the combined object is represented by v_final.
To calculate the total momentum after the collision, we use the combined mass (m_combined = m1 + m2) and the final velocity (v_final) of the combined object:
Total momentum after the collision (p_final) = m_combined * v_final
According to the principle of conservation of momentum, p_initial = p_final. Therefore:
(m1 * v1) + (m2 * v2) = m_combined * v_final
Now, let's substitute the given values and solve for v_final:
(3 kg * 10 m/s) + (5 kg * 8 m/s) = (3 kg + 5 kg) * v_final
30 kg*m/s + 40 kg*m/s = 8 kg * v_final
70 kg*m/s = 8 kg * v_final
Divide both sides of the equation by 8 kg to solve for v_final:
v_final = 70 kg*m/s / 8 kg
v_final = 8.75 m/s
Therefore, the final velocity of the combined object after the collision is 8.75 m/s.