A 1500 kg car traveling West at 90.0 km/h collides with a 1400 kg truck traveling North at 72.0 km/h.The two vehicles entangle after the collision and head off as one. What is the velocity of the wreckage immediately after the collision?
Car represents the X vector and the truck represent the Y vector.
Vfx = McVc / (Mc +Mt) because the Vx for the truck is zero
Vfy = MtVt / (Mc +Mt) because the Vy for the car is zero
draw the right triangle and then Vfc+t combo = square root of Vfx squared +Vfy squared.
Direction is using the tan function for a right triangle
Answer is 16.1 m/s or 58 km/h @ 37 degrees.
To determine the velocity of the wreckage immediately after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
Step 1: Convert the given velocities from km/h to m/s:
- Car velocity: 90.0 km/h = 25 m/s (rounded to 2 decimal places)
- Truck velocity: 72.0 km/h = 20 m/s (rounded to 2 decimal places)
Step 2: Calculate the momentum before the collision for each vehicle:
- Momentum of the car before collision = mass of the car × velocity of the car
Momentum of the car before collision = 1500 kg × 25 m/s = 37500 kg·m/s
- Momentum of the truck before collision = mass of the truck × velocity of the truck
Momentum of the truck before collision = 1400 kg × 20 m/s = 28000 kg·m/s
Step 3: Determine the total momentum before the collision:
- Total momentum before collision = momentum of the car before collision + momentum of the truck before collision
Total momentum before collision = 37500 kg·m/s + 28000 kg·m/s = 65500 kg·m/s
Step 4: Determine the total mass of the wreckage after the collision:
- Total mass of the wreckage = mass of the car + mass of the truck
Total mass of the wreckage = 1500 kg + 1400 kg = 2900 kg
Step 5: Calculate the velocity of the wreckage after the collision using the law of conservation of momentum:
- Total momentum after collision = total momentum before collision
- The velocity of the wreckage after the collision can be calculated as follows:
Total momentum after collision = total mass of the wreckage × velocity of the wreckage
Velocity of the wreckage = total momentum after collision ÷ total mass of the wreckage
Substituting the known values:
- Velocity of the wreckage = 65500 kg·m/s ÷ 2900 kg ≈ 22.59 m/s (rounded to 2 decimal places)
Therefore, the velocity of the wreckage immediately after the collision is approximately 22.59 m/s.
To find the velocity of the wreckage immediately after the collision, we need to 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 defined as the product of its mass and velocity. So, we can calculate the momentum of the car and truck separately before the collision.
Momentum of the car (P_car) = mass of the car (m_car) × velocity of the car (v_car)
= 1500 kg × 90.0 km/h
To use this equation, we need to convert km/h to m/s because the SI system uses meters and seconds.
1 km = 1000 m
1 hour = 3600 seconds
So, the velocity of the car in m/s = (90.0 km/h) × (1000 m/1 km) × (1 h/3600 s)
- You can calculate this to find the value of v_car.
Similarly, we can calculate the momentum of the truck before the collision.
Momentum of the truck (P_truck) = mass of the truck (m_truck) × velocity of the truck (v_truck)
= 1400 kg × 72.0 km/h
Convert km/h to m/s, just like we did for the car's velocity, to find the value of v_truck.
Now, we add the momenta of the car and truck to find the total momentum before the collision.
Total momentum before collision (P_total) = P_car + P_truck
Now, the total momentum after the collision is the same as the total momentum before the collision because of the principle of conservation of momentum. This means:
Total momentum after collision (P_total) = P_wreckage
We also know that the wreckage consists of both the car and the truck, which means:
Mass of wreckage (m_wreckage) = mass of car (m_car) + mass of truck (m_truck)
So, we can set up the equation:
P_total = m_wreckage × v_wreckage
Now, we can solve for v_wreckage, which is the velocity of the wreckage immediately after the collision.
west momentum = 1500 * 90
north momentum = 1400 * 72
final west momentum = 2900 Vwest
final north momentum = 2900 Vnorth
final = initial
speed = sqrt(Vwest^2 + Vnorth^2)
tan angle west of north = Vwest/Vnorth