A 500 car travelling at 45 km/hr towards west collides w/a 20000 kg truck travelling at 30 km/hr, 30 degrees south of west. if the two vehicle remain tangled together after collision, in what speed and in direction will they move?
A 500 car travelling at 45 km/hr towards west collides w/a 20000 kg truck travelling at 30 km/hr, 30 degrees south of west. if the two vehicle remain tangled together after collision, in what speed and in direction will they move?
To find the resulting speed and direction in which the vehicles move after the collision, we need to calculate the momentum before and after the collision and then combine them.
1. Calculate the momentum before the collision:
- Momentum (p) = mass (m) × velocity (v)
For the car:
- Given mass of the car (m1) = 500 kg
- Given velocity of the car (v1) = 45 km/hr = 45 × (1000/3600) m/s (conversion from km/hr to m/s)
- Momentum of the car before collision (p1) = m1 × v1
For the truck:
- Given mass of the truck (m2) = 20000 kg
- Given velocity of the truck (v2) = 30 km/hr = 30 × (1000/3600) m/s (conversion from km/hr to m/s)
- Momentum of the truck before collision (p2) = m2 × v2
2. Calculate the components of momentum for the truck before collision:
- The given truck velocity makes an angle of 30 degrees south of west, so we need to calculate its x and y components.
- The x-component (p2x) = p2 × cos(angle)
- The y-component (p2y) = p2 × sin(angle)
3. Calculate the components of momentum for the car before collision:
- The car is only traveling towards the west, so the x-component of its momentum (p1x) is equal to its momentum (p1), while the y-component (p1y) is 0.
4. Calculate the total momentum before collision:
- The total x-component momentum before collision (px) = p1x + p2x
- The total y-component momentum before collision (py) = p1y + p2y
5. Combine the masses of both vehicles after the collision:
- The total mass after collision (mtotal) = m1 + m2
6. Calculate the new velocity for the vehicles after the collision:
- The resulting velocity (vresultant) = (px^2 + py^2)^(1/2) / mtotal
7. Calculate the angle of the direction for the vehicles after the collision:
- The angle (theta) = arctan(py / px)
8. Convert the resulting velocity from m/s to km/hr:
- Resulting velocity (vresultant) = vresultant × (3600/1000) km/hr
By following these steps and plugging in the given values, you can determine the resulting speed and direction in which the vehicles move after the collision.