You are standing stationary along the side of the railroad tracks. A toy cannon shoots a baseball at 9 m/s. The cannon is mounted facing forward on the handlebars of a bike. Your friend is riding the bike from the front toward the back of a train car at 5 m/s. The train is traveling forward at 14 m/s. If the cannon fires at the moment the train passes, how fast is the baseball moving relative to your position?
To find the speed of the baseball relative to your position, we need to consider the velocities of the bike, the train, and the baseball.
The velocity of an object relative to another object is the difference between their individual velocities. In this case, the relative velocity of the baseball with respect to your position can be calculated by subtracting the velocities of the bike and the train from the velocity of the baseball.
Let's break down the problem:
1. The toy cannon shoots the baseball at a speed of 9 m/s in the forward direction.
2. Your friend is riding the bike toward the back of the train car at a speed of 5 m/s.
3. The train is traveling forward at a speed of 14 m/s.
To find the relative velocity of the baseball, we subtract the velocities of the bike and the train from the velocity of the baseball:
Relative velocity of the baseball = Velocity of the baseball - Velocity of the bike - Velocity of the train
Since the bike and the train are moving in the same direction, we subtract their velocities:
Relative velocity of the baseball = 9 m/s - 5 m/s - 14 m/s
Simplifying,
Relative velocity of the baseball = 9 m/s - (5 m/s + 14 m/s)
= 9 m/s - 19 m/s
= -10 m/s
The negative sign indicates that the baseball is moving in the opposite direction to your position.
Therefore, the baseball is moving at a speed of 10 m/s away from your position.