Math Question Stat

Question

A pedestrian hit by the driver of an automobile at 25 mph has an 80% chance of surviving the collision. At 35 mph the change of being killed as a result of the collision is 80%. How many times more energy was released in a collision at 64 mph than at 30 mph?

 (Round to at least two decimal places)

Answer 1

Kinetic Energy = 1/2 * m * v²

At 64 mph the KE released is (1/2)(m)(64^2)

At 30 mph the KE released is (1/2)(m)(30^2)

Note: this is a little bit confusing but you don't actually need to convert mph to m/s in this case since you are going to divide these quantities and the units (including the unknown masses) are going to cancel themselves out.

When you divide these quantities, the 1/2s and ms cancel (since there is one in the numerator and one in the denominator)

Therefore, the final ratio is 64²/30² = 4.5511111