Answer:
Step-by-step explanation:
Consider car 1 with mass and original speed and car 2 with mass and original speed . We can consider both cars as punctual masses. In this case, recall that the kinetic energy of a particle of mass and speed is given by the expression . Then, since car 1 has twice the mass of a second car, but only half as much kinetic energy based on the description, we have the following equations.
, .
Replacing the equation in the second one, leads to , which implies Since and assuming that both speeds are positive, then .
Given that, if both cars increase their speed by 5.5 m/s then they have the same kinetic energy, we have that
. Using the previous result, and expressing everything in terms of and we have that
(where cancells out).
Then, we have the following equation , which by algebraic calculations leads to . Since we assumed , we have that .Then,