I have a 1000W hub motor Using 48V 12Ah battery Can I go uph

I have a 1000W hub motor. Using 48V, 12Ah battery.
Can I go uphill at 15 mph on a bike? It is 30degree inclined and 200 meters long.
Will I need more batteries? How many batteries?
Assume the bike and the person sums 100kg.

Solution

Yes, it is possible.

Change in Potential Energy = mgh = 100 × 9.81 × 200 × sin(30) = 98100 J.

Kinetic Energy = 1/2 mV^2 = 0.5 × 100 × ((15 × 1.609)/3.6)^2 = 2247 J.

Time to cover 200m inclined distance = 200/6.7 = 29.832 S.

Motor Energy Requirement = 1000 × 29.832 = 29832 J.

Total Energy requirement = 98100 + 2247 + 29832 = 130,179 J.

Energy available in one battery = 48 × 12 × 3600 = 2073,600 J.

So, one battery is good enough to cover the given distance.