Final answer:
To calculate the car's velocity at the bottom of the first hill, subtract the energy lost to friction from the initial kinetic energy and use the rearranged kinetic energy formula to solve for the velocity.
Step-by-step explanation:
To determine the car's velocity at the bottom of the first hill after losing 3780 J of energy to friction, we can use the kinetic energy formula. The formula for kinetic energy (KE) is KE = 1/2 mv^2, where m is the mass of the car and v is its velocity. Given the initial kinetic energy and the energy lost to friction, we can calculate the remaining kinetic energy and then use it to find the new velocity.
Assuming we have the initial kinetic energy of the car (which is not provided in the question), we would subtract the work done by friction (3780 J) to get the final kinetic energy. Then, the velocity can be solved by rearranging the kinetic energy formula to v = sqrt(2KE/m).