Question

In: Physics

A cannon will launch balls at different angles but with the same inital velocity magnitude. If...

A cannon will launch balls at different angles but with the same inital velocity magnitude. If the cannon sits on the edge of a cliff that has a slope of 60 degrees, what is the distance along the slope of the ledge that the ball travels? If the inital velocity was 30 m/s and at which angle would the maximum distance be achieved?

Expert Solution

The situation can be visualized by

The initial vertical velocity is

The acceleration in the vertical direction is

The distance traveled in the vertical direction is

The equation of motion in the vertical direction is

The horizontal velocity throughout the motion is (there is no acceleration in the horizontal direction)

The equation of motion in the horizontal direction is

Putting this value in the first equation

Now from the diagram

Putting these values

Now, let us put the values of the constants in our problem

Now initially

So, the length along the slope is given by

So, the answer to the first part is 636.26 m.

Now, to maximize the value of l, we need to take the first derivative of the function and put it equal to zero.

The solution to this equation is

So, the maximum range along the slope is at 15^o launch angle.

genius_generous answered 6 months ago

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