A car takes 20 minutes to climb a hill at constant speed. The mass of the car is 1200 kgand the car gains gravitational potential energy at a rate of 6.0 kW. Take the acceleration ofgravity to be 10 m s-2 . What is the height of the hill?

To solve this problem, we first need to understand the relationship between power, work, and time. Power is defined as the rate of doing work or the amount of energy transferred per unit time. In this case, we know the power (P) is 6.0 kW or 6000 W, and the time (t) is 20 minutes or 1200 seconds.

The formula for power is:

P = W/t

Where W is the work done. We can rearrange this formula to solve for W:

W = P * t

Substituting the given values:

W = 6000 W * 1200 s = 7.2 * 10^6 J

The work done by the car is equal to the change in gravitational potential energy as it climbs the hill. The formula for gravitational potential energy (U) is:

U = m * g * h

Where m is the mass of the car (1200 kg), g is the acceleration due to gravity (10 m/s^2), and h is the height of the hill. We can rearrange this formula to solve for h:

h = U / (m * g)

Substituting the values:

h = 7.2 * 10^6 J / (1200 kg * 10 m/s^2) = 600 m

So, the height of the hill is 600 meters.