Acannon is fired from a castle wall at some unknown height above the ground. the cannonball leaves the cannon with speed 30.0m/s at angle 30° above the horizontal and hits the level ground at a horizontal distance 100m from the wall.
a) calculate the time it takes the cannon ball to hit the ground.
b) calculate the height of the castle wall.
c) what are the x- and y-components of the cannon ball’s velocity at the highest point of its trajectory?
d) what are the x- and y-components of the cannon ball’s velocity just before it hits the ground?
e) sketch, qualitatively, x-t, y-t, vx-t and vy-t graphs for the cannon ball’s motion.

Part a)

Part b)

Part C)

Part d)

In horizontal direction velocity will remain constant

in vertical direction we have

Explanation:

Part a)

Horizontal speed of the cannon

angle of projection

now we have

horizontal speed =

vertical speed =

now the time taken by it to cover the distance 100 m from the wall

Part b)

Since it hits the ground in the same time

so the height of the castle is given as

Part C)

At highest point of the projection

the vertical component of the velocity will become zero

so we will have

Part d)

In horizontal direction velocity will remain constant

so we have

in vertical direction we have

Part e)

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

the answer to this is proletariats.

hope this : )