# Dynamics: Cannon ball and the moving gun

• rndaryam
In summary, the cannon fires a cannon ball with a speed V0 and an angle alpha above the ground. The ball has a height hb at a time t.
rndaryam
https://postimg.org/image/z96a0jn8b/ https://postimg.org/image/z96a0jn8b/
link to image (bcs the feature doesn't work): https://postimg.org/image/z96a0jn8b/
1. Homework Statement

A cannon (mass m_c) is standing on the ground before it fires a cannon ball (mass m_b). At the time t_0=0. the cannon ball is leaviing the gun at height h_m above the ground with velocity V_0 at angle alpha. Air resistance can be neglected.

## Homework Equations

Find:
1. V_c(m_b,m_c,V_o,alpha)
2. h_b(t)
3. d(t)

## The Attempt at a Solution

This is my attempt for question 1:
we use F=m.a for only the horizontal direction and I got Vc=m_b.v_0.cos alpha / mc. Anyone can help me to solve the 2nd and 3rd question? I would appreciate it a lot. Thanks

Last edited:
rndaryam said:
https://postimg.org/image/z96a0jn8b/ https://postimg.org/image/z96a0jn8b/
link to image (bcs the feature doesn't work): https://postimg.org/image/z96a0jn8b/
1. Homework Statement

A cannon (mass m_c) is standing on the ground before it fires a cannon ball (mass m_b). At the time t_0=0. the cannon ball is leaviing the gun at height h_m above the ground with velocity V_0 at angle alpha. Air resistance can be neglected.

## Homework Equations

Find:
1. V_c(m_b,m_c,V_o,alpha)
2. h_b(t)
3. d(t)

## The Attempt at a Solution

This is my attempt for question 1:
we use F=m.a for only the horizontal direction and I got Vc=m_b.v_0.cos alpha / mc. Anyone can help me to solve the 2nd and 3rd question? I would appreciate it a lot. Thanks

You need some latex:

##V_c = \frac{m_b}{m_c} v_0 \cos(\alpha)##

Note that that is the speed of the cannon. It's clearly in the opposite direction from the ball.

For part 2, is ##h_b(t)## the height of the ball at time ##t##?

If so, how can you go about calculating that?

Hi rndaryam, Welcome to Physics Forums.

The "Relevant equations" section of the template is meant for you to list any standard equations or physics laws that you feel might pertain to or otherwise be useful in solving the problem. For example, you might list the relevant projectile motion equations and the law of conservation of momentum. What you have listed is actually part of the problem statement (the things that you need to calculate).

I've inserted a copy of your image into your post for you, so now it's visible to helpers without having to follow a link.

## 1. How does the mass of the cannon ball affect its trajectory?

The mass of the cannon ball does not have a direct effect on its trajectory. However, a heavier cannon ball will experience more air resistance and may not travel as far as a lighter cannon ball.

## 2. Does the angle of the cannon affect the distance the cannon ball travels?

Yes, the angle of the cannon does affect the distance the cannon ball travels. The optimal angle for maximum distance is typically around 45 degrees, but this can vary depending on factors such as air resistance and initial velocity.

## 3. How does the initial velocity of the cannon ball affect its motion?

The initial velocity of the cannon ball determines the initial speed and direction at which it is launched. This, along with the angle of the cannon, will determine the trajectory and distance the cannon ball travels.

## 4. What factors influence the force exerted by the moving gun on the cannon ball?

The force exerted by the moving gun on the cannon ball is influenced by the mass and velocity of the gun, as well as the angle at which it is fired. Other factors such as air resistance and gravity may also play a role.

## 5. How is the motion of the cannon ball affected by air resistance?

Air resistance affects the motion of the cannon ball by slowing it down as it travels through the air. This can cause the cannon ball to fall short of its expected distance, and may also alter its trajectory.