A(n) 2864 kg van runs into the back of a(n)
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.
M1*V1 + M2*V2 = M1*V + M2*V.
2864*V1 + 856*0 = 2864*7.5 + 856*7.5.
V1 = ?
To find the initial speed of the van, 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 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.