Imagine two inertial frames, S and S'. Inertial frame S' moves with velocity v0 = 5 m = s in the upward (positive y) direction as seen by an observer in frame S. Now imagine that a person at rest in frame S throws a ball with mass m straight up into the air with initial velocity v 0 (with respect to frame S) from an initial height of y=y0 = 0 at time t= 0. Use Galilean relativity, and take gravity into account. Use a reasonable number of signi cant digits and appropriate units.
Question 1: Does the ball appear to be moving in S'?
Q2: Acceleration in both S and S'
Q3: Max y height in S?
Q4: What is the position of the ball y'ymax according to frame S' when it reaches its maximum height ymax in frame S?
The Attempt at a Solution
So for Q1 I say that the ball does not appear to be moving. To better understand this I thought about a person in an elevator and a person in front stationary. The stationary person throws a ball up just as I pass in the elevator. During that time t>0 the ball will appear stationary since I will be essentially moving with the ball. However, since the ball has velocity v0 and I have a velocity of 5m/s this is where I thought that this may be wrong. Instead it would appear to be moving, but moving much more slowly. To understand this better I imagined the train scenario. A train is moving at 5m/s and someone throws a ball in the same direction of the train, it is moving slower since I am TRAVELLING WITH the ball essentially. Is that the correct reasoning? How would one write this in mathematics?
For Q2 I just used the kinematics equations from physics 1 and applied them to each reference frame. In the case of S it would be accelerating at 9.8 m/s with the upward direction being positive so for S it is -9.8 m/s. Now things get confusing for S'. This frame of reference IS moving WITH the ball. This means that there is a different look to it initially. I then realized that since the laws of physics match for all frames of reference wouldn't that mean the acceleration is still -9.8m/s? I am lost here.
Q3 should be h = √(1/(4.9m)) as I used (1/2)mgh and solved for h, but I think this is wrong.
Q4 is completely confusing and I have no idea where to begin or how to think about it.