Question

You’re the infamous captain of a roving band of pirates and you recently captured a castle

full of treasures. Another band of marauding pirates are trying to storm your castle. You have

a single cannon that can fire cannon balls from over the castle walls and down to the ground

below. In order to successfully hit the pirates on the ground, you need to know the

typical

launch speed of cannon ball fired from your cannon.

To determine the launch speed of the cannon ball, you fire a cannon ball and observe that the

ball hits a target

R

meters away as measured from the base of castle’s wall. The cannon ball

is fired horizontally at a height of

h

meters above the ground. Using these data, determine the

cannon ball’s time of flight

t

and its launch speed

v

0

. Your answer for time of flight should be

expressed in terms of

h

and

g

and your answer for launch speed should be expressed in

h

,

g

,

and

R

only.

Answer 1

This is a question dealing with motion in 2D.

we have range of cannon ball to be R and the height h above it's thrown.

to find the initial velocity and the time of the flight.

we have the ball thrown initially in Horizontal direction so the Y velocity is zero. There is only velocity in X direction.

The trajectory will be as given in the above picture.

the equations of motion are (hope you got the notation they are, Velocity, initial velocity, acceleration due to gravity and time)

similarly  

The range is the horizontal distance covered. So the formula for horozontal distance covered

we have the negatie sign due to accelertion due to is downwrds.

also we have final velocity is zero.

so the equation becomes

so for the vertical motion the the distance covered is h.

equation for the vertical motion is  

it is the euation for time of flight.