I have a projectile motion question. If let's say a cannon which was placed on a moving cart with negligible friction projects a cannonball straight up in the air where will it fall? Would it be behind the cannon, on the rider or fall straight down back into the cannon?
And what is the horizontal velocity of the ball relative to the rider of the cart?
ignoring air friction? It lands on the cart if the cart is in uniform horizontal motion.
Horizontal velocity is the same as the cart velocity.
Now would that also be the same visual for an observer? Or would it seem to them like the it's curving and fall on the rider?
To find out where the cannonball will fall in this scenario, we need to consider the horizontal and vertical motions separately.
First, let's analyze the vertical motion of the cannonball. When the cannonball is projected straight up, it follows a parabolic trajectory due to gravity. As it reaches the highest point, the upward velocity reduces to zero, and then it starts to fall back down. Since the cannonball was initially projected straight up, it will fall straight down back into the cannon when it returns.
Next, let's consider the horizontal motion of the cannonball relative to the rider of the cart. In this case, we need to remember that the cannonball has the same horizontal velocity as the cannon and the cart. This principle is known as the law of inertia. So, regardless of the motion of the cart, the horizontal velocity of the cannonball remains constant.
Therefore, from the perspective of the rider on the moving cart, the cannonball will fall straight down into the cannon, and its horizontal velocity relative to the rider will remain unchanged.
In summary, the cannonball will fall straight down into the cannon regardless of the motion of the cart, and its horizontal velocity relative to the rider will be constant.