Moving Reference Frames and Cannon

[fudawala]

This is the question:

A physics lecture demonstration uses a small canon mounted on a cart that moves at constant velocity v across the floor. At what angle theta should the cannon point (measured from the horizontal floor of the cart) if the cannonball is to land back in the mouth of the cannon? Explain clearly your choice of frame of reference.

 

[Fisix]

The horizontal component of the velocity of the cannonball must be equal with the velocity of the cart.

v = vbx = vb.cos θ

cos θ = v/vb

where vb is the velocity of the cannonball

obs. Considering that it happens in the vacuum so there is no drag forces from the fluid (air).

 

[m2003]

In order for the cannonball to land back in the mouth of the cannon, the cannon must be angled at a specific angle theta that takes into account the motion of the cart. This is because the cannonball will also be moving with the same velocity as the cart, and therefore, it will have a different trajectory than if the cart was at rest.

To determine the correct angle theta, we must consider the concept of relative motion and the use of moving reference frames. In this scenario, the cart and the cannonball are both moving at the same constant velocity v. This means that from the reference frame of the cart, the cannonball appears to be at rest. However, from an external reference frame (such as the floor), the cannonball will appear to be moving at a velocity v.

Therefore, when calculating the trajectory of the cannonball, we must use the reference frame of the floor to account for the motion of the cart. This means that the angle theta should be measured from the horizontal floor of the cart, as this is the reference frame in which the cannonball will be moving.

If we were to measure the angle theta from the cart's reference frame, the cannonball would appear to be moving in a straight line and would not land back in the mouth of the cannon. By using the correct reference frame, we are able to accurately calculate the trajectory of the cannonball and ensure that it lands back in the mouth of the cannon.

In conclusion, the angle theta for the cannon should be measured from the horizontal floor of the cart in order for the cannonball to land back in the mouth of the cannon. This takes into account the concept of relative motion and the use of moving reference frames, allowing for an accurate prediction of the cannonball's trajectory.