A 1200 kg car is traveling at 45 km/h and hits a 1000 kg car parked on the edge of a 70 m deep canyon. What is the velocity of the two car wreck?
momentum is conserved.
M1*V1+0=(M1+M2)V solve for V I would change km/h to m/s
M1*V1 + 0 = (m1+m2)V
1200V1+0=(1200+1000)45
1200V1 = 2200*45
1200V1 = 99000
V1 = 99000/1200
V1 = 82.5km/h
To find the velocity of the two-car wreck, 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.
Before we proceed, let's convert the velocity of the first car from km/h to m/s. To do this, we divide the speed in km/h by 3.6 since there are 3.6 seconds in an hour.
So, the velocity of the first car is:
45 km/h ÷ 3.6 = 12.5 m/s
Now, let's calculate the total momentum before the collision. The momentum (p) of an object is given by the product of its mass (m) and velocity (v). So, we can calculate the momentum of the first car and the parked car separately.
Momentum of the first car (m1):
Mass of the first car = 1200 kg
Velocity of the first car = 12.5 m/s
m1 = 1200 kg × 12.5 m/s = 15,000 kg*m/s
Momentum of the parked car (m2):
Mass of the parked car = 1000 kg
Since the parked car is at rest, its velocity is 0 m/s.
m2 = 1000 kg × 0 m/s = 0 kg*m/s
The total momentum before the collision (P1) is the sum of the individual momenta:
P1 = m1 + m2 = 15,000 kg*m/s + 0 kg*m/s = 15,000 kg*m/s
According to the principle of conservation of momentum, the total momentum after the collision (P2) is equal to P1.
Now, in this scenario, the cars are falling into a canyon. This means that the collision is an inelastic collision. In an inelastic collision, the two objects stick together after the impact, forming a single combined mass. Therefore, the two cars become one combined mass.
The combined mass (M) after the collision is the sum of the individual masses:
M = m1 + m2 = 1200 kg + 1000 kg = 2200 kg
We need to find the velocity (V) of the combined mass. Since momentum (P) is the product of mass (M) and velocity (V), we can rearrange the equation to solve for V:
P2 = M × V
Substituting the values we've calculated:
15,000 kg*m/s = 2200 kg × V
Now, we can solve for V:
V = 15,000 kg*m/s ÷ 2200 kg ≈ 6.82 m/s
So, the velocity of the two-car wreck after the collision is approximately 6.82 m/s.