A train of mass `2xx10^(5)` kg has a constant speed of 20 `ms^(-1)` up a hill inclined at `theta=sin^(-1)((1)/(50))` to the horizontal when the engine is working at `8xx10^(5)` W. Find the resistance to motion of the trian. (Take ,g=9.8 `ms^(-2)`).

Explanation

To solve the problem step-by-step, we will follow these steps:

### Step 1: Identify the given data
- Mass of the train, \( m = 2 \times 10^5 \, \text{kg} \)
- Speed of the train, \( v = 20 \, \text{m/s} \)
- Power of the engine, \( P = 8 \times 10^5 \, \text{W} \)
- Angle of incline, \( \theta = \sin^{-1}\left(\frac{1}{50}\right) \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
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