A 1000-kg car is travelling west at 17.0 m/s toward an intersection. A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection. The car and truck collide at the intersection and stick together. What is their speed after the collision?
Question
A 1000-kg car is travelling west at 17.0 m/s toward an intersection. A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection. The car and truck collide at the intersection and stick together. What is their speed after the collision?
Solution
To solve this problem, we need to use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Step 1: Calculate the momentum of each vehicle before the collision.
Momentum is calculated as the product of mass and velocity.
For the car: P_car = m_car * v_car = 1000 kg * 17.0 m/s = 17000 kg*m/s
For the truck: P_truck = m_truck * v_truck = 1500 kg * 20.0 m/s = 30000 kg*m/s
Step 2: Determine the total momentum before the collision.
The car is moving west and the truck is moving north. These are perpendicular directions, so we can treat this as a right triangle and use the Pythagorean theorem to find the total momentum.
P_total = sqrt((P_car)^2 + (P_truck)^2) = sqrt((17000 kgm/s)^2 + (30000 kgm/s)^2) = 35000 kg*m/s
Step 3: Calculate the total mass after the collision.
The car and truck stick together after the collision, so their masses add together.
m_total = m_car + m_truck = 1000 kg + 1500 kg = 2500 kg
Step 4: Calculate the speed after the collision.
Speed is calculated as momentum divided by mass.
v_total = P_total / m_total = 35000 kg*m/s / 2500 kg = 14 m/s
So, the speed of the car and truck together after the collision is 14 m/s.
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A 1000-kg car is travelling west at 17.0 m/s toward an intersection. A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection. The car and truck collide at the intersection and sick together. What is the angle of their velocity after the collision relative to the east direction?
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