A 1400 kg car moving south at 11.5 m/s collides with a 2800 kg car moving north. The cars stick together and move as a unit after the collision at a velocity of 5.24 m/s to the north. Find the velocity of the 2800 kg car before the collision.
m1 •v1 - m2•v2 = - (m1+m2) •u,
v2 ={ m1 •v1 + (m1+m2) •u}/m2 =
={(1400•11.5) + 1400+2800) •5.24}/2800 = =13.61 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Let's assume the velocity of the 2800 kg car before the collision is v1. The momentum of the 1400 kg car moving south at 11.5 m/s is (-1400 kg) * (11.5 m/s) = -16100 kg*m/s (negative sign indicates opposite direction).
The total momentum before the collision is the sum of the two cars' momenta: -16100 kg*m/s + (2800 kg * v1).
After the collision, the cars stick together and move as a unit with a velocity of 5.24 m/s to the north. The total momentum after the collision is the mass of the combined cars (1400 kg + 2800 kg = 4200 kg) multiplied by their common final velocity (5.24 m/s): 4200 kg * 5.24 m/s = 22008 kg*m/s.
According to the principle of conservation of momentum, the total momentum before the collision (-16100 kg*m/s + 2800 kg * v1) should be equal to the total momentum after the collision (22008 kg*m/s).
Therefore, we can write the equation:
-16100 kg*m/s + 2800 kg * v1 = 22008 kg*m/s.
To find the velocity of the 2800 kg car before the collision (v1), we can rearrange the equation:
2800 kg * v1 = 22008 kg*m/s + 16100 kg*m/s,
2800 kg * v1 = 38108 kg*m/s,
v1 = 38108 kg*m/s / 2800 kg.
Simplifying the expression, we find:
v1 = 13.6107 m/s (rounded to four decimal places).
Therefore, the velocity of the 2800 kg car before the collision is approximately 13.6107 m/s.