A 4.0 x 10^4 N Tortilla Chip Van moving west at a velocity of 8.0 m/s collides with a 3.0 x 10^4 N Nacho Cheese Van heading south at a velocity of 5.0 m/s. If these two vehicles lock together upon impact and make doritios, what is their velocity?
To find the velocity of the Doritos after the collision, we can use the principle of conservation of momentum.
The total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity.
Momentum of Tortilla Chip Van before collision:
= Mass x Velocity
= (4.0 x 10^4) kg x 8.0 m/s
= 3.2 x 10^5 kg·m/s
Momentum of Nacho Cheese Van before collision:
= Mass x Velocity
= (3.0 x 10^4) kg x 5.0 m/s
= 1.5 x 10^5 kg·m/s
Total momentum before collision:
= 3.2 x 10^5 kg·m/s (west) + 1.5 x 10^5 kg·m/s (south)
After colliding, the two vans lock together and move as one. Let's assume their combined mass is M and the final velocity after the collision is V.
Total momentum after collision:
= M x V
According to the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
3.2 x 10^5 kg·m/s (west) + 1.5 x 10^5 kg·m/s (south) = M x V
Since momentum is a vector quantity, we must consider the direction of the motion of van after collision. The resultant velocity can be represented as the vector sum of the velocities of individual vans.
Using the Pythagorean theorem:
V^2 = (V_west)^2 + (V_south)^2
V = sqrt((8.0 m/s)^2 + (5.0 m/s)^2)
V = sqrt(64 + 25)
V = sqrt(89) = 9.43 m/s
Therefore, the velocity of the Doritos after collision is 9.43 m/s in the direction at an angle tan^(-1)(5.0/8.0) = 31.01 degrees south of west.