A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is `prop = 30^@` and the angle of the barrel to the horizontal `beta = 60^@`. The initial velocity `v` of the shell is `21 m s^-1`. Then find the distance of point from the gun at which the shell will fall.

Explanation

To solve the problem, we need to determine the distance from the gun to the point where the shell will land when fired along the slope of a hill. Here’s a step-by-step solution:

### Step 1: Understand the Geometry of the Problem
We have a hill with a slope angle \( \alpha = 30^\circ \) and the gun is fired at an angle \( \beta = 60^\circ \) to the horizontal. We need to find the angle \( \theta \) between the direction of the shell and the slope of the hill.

### Step 2: Calculate the Effective Angle
The effective angle \( \theta \) at which the shell is fired with respect to the slope can be calculated as:
\[
...