# Calculating energy needed for by a car climbing a slope [closed]

I'm having a difficult time answering this question. I think I'm just converting the units wrong somewhere:

You're the CEO of a courier company, and you decide to select an electric car for your fleet of vehicles. A particular car has a mass of 1600kg and is powered by 26 12−V batteries connected in series, for a total of 312 V. Batteries are rated at 100 ampere-hours, which means they can deliver 100 A for 1 h, 1 A for 100 h, or any combination that equals 100A⋅h. When the batteries are connected in series, the charge output of all the batteries is the same as one battery-in this case 100A⋅h. The motor is 85% efficient in converting electrical energy to mechanical energy in the drive wheels. A test report says the car can climb a 12∘ slope at a speed of 50km/h. How long can the car maintain that speed at this angle?

I'm using mgsin12 to calculate the force of gravity acting on the car and 100*.85*312 to calculate the power delivered by the battery. My confusion lies in how I should incorporate 50km/h to solve the problem.

## closed as off-topic by user10851, Qmechanic♦Nov 14 '13 at 17:52

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I think there's an easy way to do this. Work out how much energy the batteries store and multiply by 0.85 to get the energy delivered to the wheels. This energy will be the same as the change in potential energy of the car, $V = mgh$, where $h$ is the distance the car has moved vertically upwards. When you've calculated $h$ divide it by the vertical component of the car's velocity, $v \sin\theta$, and you get the time.