Relative velocity of a ball on a train

• MickeyBlue
In summary: But then I read about inertial frames and it seems like it would make a big difference. What is your opinion?
MickeyBlue

Homework Statement

A train is traveling east along a straight run of track at 72.0 km/hr. Inside, two siblings 1.9 m apart are playing catch directly across the aisle. The kid wearing a P.J.Harvey T-shirt throws the ball horizontally north. The ball crosses the train and is caught 0.75 s later by her little brother. (Ignore any effects of gravity or friction.) Find the magnitude of the ball's velocity from the little brother's point of view.

Homework Equations

1. xf = xi + ViΔt + 1/2ax(Δt)2
2. a2 = b2 + c2

The Attempt at a Solution

I used the first equation to calculate the velocity of the ball in the y-axis. I assumed that xi = ax = 0 and got 2.5 m/s. I then used Pythagoras and head-to-tail vector addition to get the actual speed and direction of the ball, taking speed in the x-axis as the speed of the train (20m/s). I took the brother to be moving at the same speed and direction as the train. My final answer was 40 m/s.

I know this is the wrong answer but I can't work out why. Any advice?

What about a simpler question; what is the balls velocity from the boy's point of view before the ball is thrown? Is the ball moving relative to the boy?

The velocity of the train is irrelevant as the boy, girl, and train are not moving relative to each other. Similarly, if they were playing catch at the train station the Earth's motion relative to the sun or the solar systems velocity relative to the centre of the milky way isn't relevant: the velocity the boy sees is relative to himself.

billy_joule said:
What about a simpler question; what is the balls velocity from the boy's point of view before the ball is thrown? Is the ball moving relative to the boy?

The velocity of the train is irrelevant as the boy, girl, and train are not moving relative to each other. Similarly, if they were playing catch at the train station the Earth's motion relative to the sun or the solar systems velocity relative to the centre of the milky way isn't relevant: the velocity the boy sees is relative to himself.
That was the way I thought about it at first, which got me my 2.5 m/s. I thought because the boy was "technically" stationary it wouldn't affect the true velocity of the ball.

1. What is relative velocity?

Relative velocity is the velocity of an object with respect to another object. It takes into account the motion of both objects and is measured from the perspective of one of the objects.

2. How does the velocity of a ball on a moving train change?

The velocity of a ball on a moving train is affected by both the velocity of the train and the velocity of the ball. As the train moves, the ball's velocity will change relative to the ground, but its velocity relative to the train will remain constant.

3. Does the direction of the train affect the ball's velocity?

Yes, the direction of the train will affect the ball's velocity. If the train is moving in the same direction as the ball, the ball's velocity will appear to be slower. If the train is moving in the opposite direction, the ball's velocity will appear to be faster.

4. How is relative velocity calculated?

Relative velocity can be calculated by subtracting the velocity of one object from the velocity of the other object. For example, if the train is moving at 50 km/h and the ball is moving at 10 km/h in the same direction, the relative velocity of the ball would be 40 km/h.

5. Can relative velocity be negative?

Yes, relative velocity can be negative. This occurs when two objects are moving in opposite directions and their velocities are subtracted. A negative relative velocity indicates that the two objects are moving away from each other.

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