An automobile accident investigator needs to determine the initial westerly velocity of jeep (m=1720 kg) that may have been speeding before colliding head-on with a Volkswagen (m=1510 kg) that was moving with a velocity of 75.7 km/h east. The speed limit on this road is 90 km/h. After the collision, the jeep and the Volkswagen stuck together and continued to travel with a velocity of 15.5 km/h west.
a) Find the initial westerly velocity of the jeep.
b) Was the jeep speeding?
initial momentum west
= 1720 v -1510(75.7)
= final momentum west
= (1720+1510)15.5
a jeep with the voicing of 1720kg collided with a volkswagen m=1510kg that was moving 75.7 km/east. The speed limit on the Road was 90km/h leaving the jeep and the volkswagen stuck together continuing with the volicity of 15.5 km.west. I need the anwser written step by step finding the volicity of the jeeps original speed?
M(j)V(j)-M(v)V(v)=(M(j)+M(v))V' M(j)=m-jeep, M(v)=m-Volkswagen
1720V(j)-1510(75.7)=(1720+1510)15.5 V(j)= jeep's velocity
1720V(j)-114307=50065 V(v)=Volkswagen's velocity
1720V(j)=164372 V'=velocity of jeep & Volkswagen
V(j)=95.5 km/h
To find the initial westerly velocity of the jeep, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Momentum is defined as the product of an object's mass and its velocity.
Given:
Mass of the jeep (m1) = 1720 kg
Mass of the Volkswagen (m2) = 1510 kg
Velocity of the Volkswagen before the collision (v2) = 75.7 km/h east
Velocity of the combined masses after the collision (v3) = 15.5 km/h west
a) Find the initial westerly velocity of the jeep:
Step 1: Convert the velocities from km/h to m/s.
Velocity of the Volkswagen before the collision (v2) = 75.7 km/h = 75.7 * (1000/3600) m/s = 21.03 m/s
Velocity of the combined masses after the collision (v3) = 15.5 km/h = 15.5 * (1000/3600) m/s = 4.30 m/s
Step 2: Apply the conservation of momentum formula:
(mass of the jeep * initial velocity of the jeep) + (mass of the Volkswagen * initial velocity of the Volkswagen) = (combined mass * final velocity)
(1720 kg * initial velocity of the jeep) + (1510 kg * 21.03 m/s) = (3230 kg * 4.30 m/s)
Step 3: Solve for the initial velocity of the jeep:
(1720 kg * initial velocity of the jeep) + (1510 kg * 21.03 m/s) = (3230 kg * 4.30 m/s)
(1720 kg * initial velocity of the jeep) = (3230 kg * 4.30 m/s) - (1510 kg * 21.03 m/s)
Initial velocity of the jeep = [(3230 kg * 4.30 m/s) - (1510 kg * 21.03 m/s)] / 1720 kg
Solving this equation will give us the initial westerly velocity of the jeep.
b) To determine if the jeep was speeding, we need to compare the initial velocity of the jeep with the speed limit of 90 km/h. If the initial velocity is greater than 90 km/h, then the jeep was speeding. If it is equal to or less than 90 km/h, the jeep was not speeding.