To determine the initial speed of the truck, we analyze the conservation of momentum before and after the collision. Using this principle and trigonometry, we can calculate the magnitude of the velocity components in the east and north directions for the wreckage after the collision. From there, we can solve for the initial speed of the truck.
In order to determine the initial speed of the truck, we need to analyze the conservation of momentum before and after the collision.
Before the collision, the car and truck have initial velocities in the east and north directions, respectively. The car has a mass of 980 kg and a velocity of 22.3 m/s in the east direction, while the pickup truck has a mass of 1500 kg and a velocity of 0 m/s in the north direction.
After the collision, the wreckage moves off at 45.0 degrees above the x-axis, which means it has a velocity component in the east direction and a velocity component in the north direction. We need to find the magnitude of these velocity components.
Using the laws of conservation of momentum, we can set up equations for the total momentum before the collision and the total momentum after the collision:
Before collision: Momentum of car = mass of car * velocity of car = 980 kg * 22.3 m/s
Before collision: Momentum of truck = mass of truck * velocity of truck = 1500 kg * 0 m/s
After collision: Momentum of wreckage = (mass of car + mass of truck) * velocity of wreckage
Since the wreckage moves off at 45.0 degrees above the x-axis, we can use trigonometry to determine the magnitude of the velocity components:
Velocity component in the east direction = velocity of wreckage * cos(45)
Velocity component in the north direction = velocity of wreckage * sin(45)
Substituting these values into the equation for the total momentum after the collision and solving for the velocity of the wreckage, we can then determine the initial speed of the truck.