suppose the two cars are headed in the same direction. A 1200kg car travels at 65 mph and a 1000kg car travels at 75mph. The faster car rear-ends the slower car and their bumpers catch so that they continue moving after the collision at the same speed. Use the concepts above to detemine their final velocity
The image behind a convex mirror (radius of curvature = 71.0 cm) is located 23.0 cm from the mirror. (a) Where is the object located (give the distance to the mirror) and (b) what is the magnification of the mirror?
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To determine the final velocity of the two cars after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity: momentum = mass * velocity.
Given:
- Mass of the first car (1200 kg)
- Velocity of the first car before the collision (65 mph)
- Mass of the second car (1000 kg)
- Velocity of the second car before the collision (75 mph)
Step 1: Convert the velocities from mph (miles per hour) to m/s (meters per second).
To convert mph to m/s, we need to multiply the velocity value by 0.44704 (1 mph = 0.44704 m/s).
Velocity of the first car before the collision:
65 mph * 0.44704 m/s = 29.0576 m/s (approximately)
Velocity of the second car before the collision:
75 mph * 0.44704 m/s = 33.528 m/s (approximately)
Step 2: Calculate the total momentum before the collision.
Momentum of the first car before the collision = mass of the first car * velocity of the first car
Momentum of the first car before the collision = 1200 kg * 29.0576 m/s
Momentum of the second car before the collision = mass of the second car * velocity of the second car
Momentum of the second car before the collision = 1000 kg * 33.528 m/s
Step 3: Calculate the total momentum after the collision.
Since the two cars stick together after the collision and move at the same speed, the total mass will be the sum of their masses.
Total mass after the collision = mass of the first car + mass of the second car
Total mass after the collision = 1200 kg + 1000 kg
Step 4: Using the principle of conservation of momentum, set the total momentum before the collision equal to the total momentum after the collision.
Total momentum before the collision = Total momentum after the collision
(1200 kg * 29.0576 m/s) + (1000 kg * 33.528 m/s) = Total mass after the collision * final velocity
Solving the equation for the final velocity will give us the answer.