# Projectile motion of a cannon ball

• Ry122
In summary, a ball is fired from a cannon at an angle of 40 degrees to the horizontal with an initial velocity of 48.8 m/s. It travels 300m before hitting the side of a cliff which is 10 meters higher than the cannon's position. The ball has a negative velocity when it hits the cliff.
Ry122
a ball is fired from a cannon at an angle of 40 degrees to the horizontal and it travels 300m before hitting the side of a cliff which is 10 meters higher than the cannons position.
Determine the initial velocity.

The ball has a negative velocity when it hits the cliff.

My attempt:
Where v = the balls initial velocity
y component of velocity = -9.81t + Vsin40

integrate this and get

y position = .5*-9.8t^2 + vsin40t

x component of velocity = vcos40

integrate this and get

x position = vcos40tUsing the expression for x velocity, solve for t at 300m in the x direction and get the expression
t=300/vcos40

Sub this into the expression for the y position above and solve for v.I'm unsure if this is the correct way to go about doing this. The velocity I ended up with is 42.7124ms^-1 which seems a bit slow for the distance it covers.

I check your answer, but I got the initial speed is 48.8 m/s.

## What is projectile motion?

Projectile motion refers to the motion of an object (in this case, a cannon ball) that is launched into the air and moves under the influence of gravity alone, with no additional forces acting upon it.

## What factors affect the trajectory of a cannon ball?

The trajectory of a cannon ball is affected by the initial velocity of the ball, the angle at which it is launched, the force of gravity, and any external factors such as air resistance.

## How do you calculate the range of a cannon ball?

The range of a cannon ball can be calculated using the formula R = (v^2 * sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## Why does a cannon ball follow a curved path?

A cannon ball follows a curved path due to the force of gravity pulling it towards the ground. As the ball moves forward, it is also pulled downwards, resulting in a parabolic trajectory.

## Can the trajectory of a cannon ball be affected by air resistance?

Yes, air resistance can affect the trajectory of a cannon ball. As the ball moves through the air, it experiences a force in the opposite direction of its motion, causing it to slow down and potentially alter its path.

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