a truck with a mass of 5000 kg and a velocity of 15.0 m/s collides head-on with a car whose mass is 1000 kg, moving at 30.0 m/s. if the two vehicles move together after the impact, at what velocity do they move?
M1*V1 + M2*V2 = M1*V + M2*V.
5000*15 + 1000*(-30) = 5000V + 1000V.
V = ?.
To find the velocity at which the vehicles move together after the impact, you need to apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Therefore, the momentum (p1) of the truck before the collision is given by:
p1 = mass of truck × velocity of truck
= 5000 kg × 15.0 m/s
= 75000 kg·m/s
Similarly, the momentum (p2) of the car before the collision is:
p2 = mass of car × velocity of car
= 1000 kg × 30.0 m/s
= 30000 kg·m/s
The total momentum before the collision (p_total_before) is the sum of p1 and p2:
p_total_before = p1 + p2
= 75000 kg·m/s + 30000 kg·m/s
= 105000 kg·m/s
Since momentum is conserved, the total momentum after the collision (p_total_after) is the same as p_total_before:
p_total_after = p_total_before
= 105000 kg·m/s
Now, the total mass (m_total) after the collision is the sum of the masses of the truck and the car:
m_total = mass of truck + mass of car
= 5000 kg + 1000 kg
= 6000 kg
To find the velocity (v_total) at which the two vehicles move together after the impact, divide the total momentum after the collision by the total mass after the collision:
v_total = p_total_after / m_total
= 105000 kg·m/s / 6000 kg
≈ 17.5 m/s
Therefore, the truck and the car move together after the impact at a velocity of approximately 17.5 m/s.