Answer:
110 m
46.5 m/s
Explanation:
The total energy of the car is conserved during the descent, so the kinetic energy at the bottom of the hill is equal to the potential energy at the top of the hill. The potential energy is equal to the weight of the car times the height of the hill, and the kinetic energy is equal to half the mass times the square of the speed. Using these equations, we can solve for the height of the hill and the speed of the car.
Energy is conserved:
PE = KE
mgh = KE
h = KE / mg
h = (3.13×10⁵ J) / (290 kg × 9.8 m/s²)
h = 110 m
Definition of kinetic energy:
KE = ½ mv²
v = √(2KE / m)
v = √(2 (3.13×10⁵ J) / (290 kg))
v = 46.5 m/s
Notice both the height of the hill and the speed of the car are independent of the time it takes the car to descend.
