We have 2 cars. Car "A" and car "B"
if car A weighs 3180 lbs If car "B" weighes 2000 pounds
How fast would car "A" have to travel to knock car "B" 32 feet?
depends. On ice? at the edge of a cliff? next to a brick wall? on a wet highway?
It is neither math, nor physics.
plain dry road
To determine how fast Car "A" would have to travel to knock Car "B" a distance of 32 feet, we can use the principles of conservation of momentum and the equation of motion.
First, let's assume that the collision between Car "A" and Car "B" is an elastic collision, meaning that both momentum and kinetic energy are conserved.
The equation for the conservation of momentum is:
(mass of Car "A" × velocity of Car "A" before collision) + (mass of Car "B" × velocity of Car "B" before collision) = (mass of Car "A" × velocity of Car "A" after collision) + (mass of Car "B" × velocity of Car "B" after collision)
Since Car "B" is initially at rest, we can simplify the equation to:
(mass of Car "A" × velocity of Car "A" before collision) = (mass of Car "A" × velocity of Car "A" after collision) + (mass of Car "B" × velocity of Car "B" after collision)
The equation of motion we can use is:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
In this case, the distance is 32 feet, the initial velocity of Car "A" is zero since it is initially at rest, and the acceleration is the unknown factor we need to determine. Rearranging this equation, we get:
0.5 × Acceleration × Time^2 = -32 feet
Since we want to find the time it takes for Car "A" to reach Car "B" while traveling a distance of 32 feet, we can substitute the equation for time into the first equation of momentum conservation:
(mass of Car "A" × velocity of Car "A" before collision) = (mass of Car "A" × velocity of Car "A" after collision) + (mass of Car "B" × velocity of Car "B" after collision)
Substituting the distance equation into time and solving for acceleration, we get:
0.5 × Acceleration × (-32 feet / Acceleration^2) = -32 feet
-16 = -32
Acceleration = 2 feet per second squared
Now, we have the acceleration value. We can use it to find the velocity of Car "A" after collision by rearranging the equation of motion:
Distance = Initial velocity × Time + 0.5 × Acceleration × Time^2
32 feet = Initial velocity × Time + 0.5 × 2 feet per second squared × Time^2
We can solve this equation to find the value for time, and then substitute it back into the equation to find the velocity of Car "A" after collision.
So, based on the given information, the weight of Car "A" is 3180 pounds and the weight of Car "B" is 2000 pounds. The acceleration required to knock Car "B" a distance of 32 feet is 2 feet per second squared. From here, you can use the equations and calculations explained above to find the velocity of Car "A" after collision.