M1*V1 + M2*V2 = M1*V + M2*V.
2864*V1 + 856*0 = 2864*7.5 + 856*7.5.
V1 = ?
856 kg compact car at rest. They move of together at 7.5 m/s. Assuming no friction
with the ground, find the initial speed of the
van.
Answer in units of m/s.
2864*V1 + 856*0 = 2864*7.5 + 856*7.5.
V1 = ?
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is calculated using the formula:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Let's denote the initial velocity of the van as Vv and the initial velocity of the compact car as Vc. Given the following information:
Mass of the van (m1) = 2864 kg
Mass of the compact car (m2) = 856 kg
Final velocity of both vehicles (vf) = 7.5 m/s
Before the collision:
The momentum of the van (p1) = m1 * Vv
The momentum of the compact car (p2) = m2 * 0 (as it is at rest)
After the collision:
The momentum of the van (p1') = (m1 + m2) * vf (as both vehicles move together)
The momentum of the compact car (p2') = 0 (as it has stopped moving)
According to the principle of conservation of momentum, p1 + p2 = p1' + p2'
m1 * Vv + 0 = (m1 + m2) * vf + 0
Rearranging the equation:
Vv = [(m1 + m2) * vf] / m1
Substituting the values:
Vv = [(2864 kg + 856 kg) * 7.5 m/s] / 2864 kg
Now, calculating the value:
Vv = (3720 kg * 7.5 m/s) / 2864 kg
Vv = 9750 kg m/s / 2864 kg
Vv ≈ 3.4 m/s
Therefore, the initial speed of the van, Vv, is approximately 3.4 m/s.