Answer to Question #97789 in Physics for Nyx

Question

The engine of a 2000 kg Mercedes going up
Pike’s Peak delivers energy to its drive wheel
at the rate 100 kW .
Neglecting air resistance, what is the largest
speed the car can sustain on the steep Pike’s
Peak mountain highway, where the road is 30◦
to the horizontal? The acceleration due to
gravity is 10 m/s
2.
1. 10 m/s
2. 20 m/s
3. 100 m/s
4. 40 m/s
5. 0 m/s

Answer 1

The power is

$$P=Fv=mg\sin{30}v=0.5mgv$$

$$v=\frac{2P}{mg}$$

$$v=\frac{2(100000)}{(2000)(10)}=10\frac{m}{s}$$