Truck moves with a velocity of 43 m\s and collides with the stationary car with exactly 1 / 5 of its mass. If the two vehicles are locked together, calculate the magnitude of the velocity of their combined masses immediately after the collision?
To solve this problem, we can 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.
Initially, the truck has a velocity of 43 m/s and the car is stationary. Let's assume the mass of the truck is "m" and the mass of the car is "m/5".
The total momentum before the collision can be calculated as:
Initial momentum = (Mass of the truck * Velocity of the truck) + (Mass of the car * Velocity of the car)
= (m * 43 m/s) + ((m/5) * 0 m/s) [because the car is stationary]
Since the car is stationary, its initial velocity is 0 m/s.
Now, after the collision, the truck and car are locked together. Let's assume the combined mass after the collision is "M", and the final velocity is "V".
The total momentum after the collision can be calculated as:
Final momentum = Combined mass * Final velocity
= M * V
According to the conservation of momentum, the initial momentum is equal to the final momentum:
Initial momentum = Final momentum
(m * 43 m/s) + ((m/5) * 0 m/s) = M * V
To solve for V, we need to rearrange the equation:
V = (m * 43 m/s) / M
However, we still need to find the value of M. Since the truck and car are locked together, the combined mass can be calculated as:
Combined mass = Mass of the truck + Mass of the car
= m + m/5
= (6m + m) / 5
= 7m / 5
Now we can substitute the value of M back into the equation for V:
V = (m * 43 m/s) / (7m / 5)
Simplifying further:
V = (m * 43 m/s) * (5 / (7m))
V = (215 m^2/s) / 7
V ≈ 30.71 m/s
Therefore, the magnitude of the velocity of the combined masses immediately after the collision is approximately 30.71 m/s.