A 7900 kg truck traveling east at 5 m/s collides with a 1650 kg car traveling 300 south of west at 20 m/s. After the collision at what angle do the two vehicles move. Express you answer in degrees from the positive x-axis. Use a coordinate where north is the +y axis and east is the +x axis.
suspect you mean 30 south of west
momentum east 7900*5 - 1650*20 cos 30
momentum south 1650*20 sin 30
new mass = 7900 + 1650
new mass*speed east = old momentum east
new mass* speed south = old momentum south
To determine the angle at which the two vehicles move after the collision, we need to analyze the momentum conservation during the collision and then calculate the resulting angle.
1. Calculate the initial momentum of the truck and car:
Momentum = mass * velocity
Initial momentum of the truck (east) = 7900 kg * 5 m/s = 39500 kg·m/s (east)
Initial momentum of the car (south of west) = 1650 kg * 20 m/s = 33000 kg·m/s (south of west)
2. Convert the car's momentum into its x and y components:
x-component of the initial momentum = Initial momentum * cos(angle)
y-component of the initial momentum = Initial momentum * sin(angle)
Given:
Angle = 300 degrees (south of west)
Initial momentum of the car = 33000 kg·m/s (south of west)
x-component of the initial momentum of the car = 33000 kg·m/s * cos(300)
y-component of the initial momentum of the car = 33000 kg·m/s * sin(300)
3. Calculate the total momentum in the x and y directions before and after the collision:
Momentum is conserved in collisions, meaning the total momentum before the collision equals the total momentum after the collision.
Total initial momentum in the x-direction = Initial momentum of the truck (east) + x-component of the initial momentum of the car
Total initial momentum in the y-direction = y-component of the initial momentum of the car
Total final momentum in the x-direction = Final momentum of the truck (east) + Final momentum of the car (x-component)
Total final momentum in the y-direction = Final momentum of the car (y-component)
Total initial momentum in the x-direction = Total final momentum in the x-direction
Total initial momentum in the y-direction = Total final momentum in the y-direction
4. Calculate the final momentum of the truck and car:
Let the final velocity of the truck be v1 and the final velocity of the car be v2.
Final momentum of the truck (east) = mass of the truck * final velocity of the truck
Final momentum of the car (x-component) = mass of the car * final velocity of the car * cos(angle)
Final momentum of the car (y-component) = mass of the car * final velocity of the car * sin(angle)
5. Apply momentum conservation to solve for v1 and v2:
Equate the total initial momentum in both x and y directions to the total final momentum.
6. Calculate the magnitude and direction of the final velocity vector:
Use the Pythagorean theorem to find the magnitude of the final velocity vector:
Final velocity (magnitude) = sqrt(v1^2 + v2^2)
Calculate the angle of the final velocity vector with the positive x-axis using trigonometry:
Final velocity (angle) = atan(v2 / v1)
7. Convert the angle to degrees:
Final angle (degrees) = Final velocity (angle) * (180 / pi)
By following these steps and calculating the momenta and velocities involved, you will be able to find the angle at which the two vehicles move after the collision.
M1*V1 + M2*V2 = M1*V + M2*V.
7900*5 + 1650*20[30o+180o] = 7900V+1650V
39500 + 33,000[210o] = 9550V
39,500 -28,579 - 16,500i = 9550V.
10,921 - 16,500i = 9550V.
19,787[-56.5o] = 9550V.
V = 2.07m/s.[-56.5o] S. of E. =
2.07m/s[304o] CCW from +x-axis.