Solving Motion of a Ball Fired by Compressed Air

[grothem]

Compressed air is used to fire a 50g ball vertically upward from a 1.0-m-tall tube. The air exerts an upward force of 2.0N on the ball as long as it is in the tube.



How high does the ball go above the top of the tube?



I used ma=F+mg to find acceleration and came up with 30.2 m/s^2. I think from here I need to use a kinematics equation to get the velocity of the ball just as it leaves the tube, but to find the height? I only have acceleration, I don't know which equation to use.

 

[Shooting Star]

Use the one connecting initial and final velos, g and the height.

 

[Moetasim]

I would suggest using the kinematic equation for displacement, which is d = vi*t + 1/2*a*t^2. In this equation, d represents the displacement or height, vi represents the initial velocity (which is 0 since the ball starts from rest), a represents the acceleration (which you have calculated to be 30.2 m/s^2), and t represents the time. Plugging in these values, we get d = 0 + 1/2 * 30.2 * t^2.

To find the time, we can use another kinematic equation, vf = vi + a*t, where vf represents the final velocity (which is also 0 since the ball stops at its maximum height), vi represents the initial velocity (again, 0), a represents the acceleration (30.2 m/s^2), and t represents the time. Solving for t, we get t = vf/a = 0/30.2 = 0 seconds.

Therefore, the ball reaches its maximum height in 0 seconds, and we can plug this value back into our first equation to find the displacement or height. d = 0 + 1/2 * 30.2 * (0)^2 = 0 meters. This means that the ball reaches a maximum height of 0 meters, which makes sense since it is fired vertically upward from a 1.0-m-tall tube.

In order to find the height above the top of the tube, we need to add the initial height of the tube to the maximum height of the ball. So the final answer would be 1.0 meters.

I would also like to note that this calculation assumes ideal conditions and does not take into account factors such as air resistance, which may affect the actual height reached by the ball. Further experimentation and data collection may be necessary for a more accurate calculation.