What velocity do the children measure for the ball when thrown at half the speed of a train moving at 70 mph?

To determine the velocity that the children measure for the ball thrown at half the speed of a train moving at 70 mph, it is essential to analyze the context of the scenario.

The train is moving at a speed of 70 mph. Half of this speed is 35 mph. When the children throw the ball at 35 mph, the direction of the throw is crucial in interpreting the velocity. If the children are positioned such that the ball is thrown in the opposite direction of the train's movement, the velocity of the ball would be measured as negative. This is because velocity is directional, and when the object moves against the direction of the reference point (in this case, the train), it can be considered as having a negative velocity relative to that point.

Thus, when children throw the ball at a speed of 35 mph in the opposite direction of the train's motion, they would measure it as −35 mph. This negative value indicates that the ball is moving away from the reference point of the train, which is crucial for understanding how velocity is assessed in a relative context.