A passenger in a train traveling at 17 m/s relative to the Earth throws a baseball at 15 m/s in the direction opposite the motion of the train. What's the velocity of the baseball relative to Earth as it leaves the thrower's hand.
The velocity of an object measured by an observer is the sum of velocities it is moving at relative to the observer. For example if an object is moving at a velocity v1 to the right relative to the observer and also has a velocity v2 to the left, the net velocity measured by the observer is (v1 - v2) to the right.
Here, the passenger is traveling in a train an moves at 17 m/s relative to the Earth. A baseball is thrown by the passenger in a direction opposite to that in which the train is traveling at 15 m/s.
The net velocity of the baseball when it leaves the passenger's hand is the sum of its velocity relative to the Earth. That is 17 + (-15), (one of the velocities has a negative sign as it is opposite in direction to the other).
This gives the velocity of the baseball relative to the Earth when it leaves the thrower's hand as 2 m/s.