QPage 48-49: Q12: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q12 Solution: A player hits a baseball at some angle. The ball goes high up…
A player hits a baseball at some angle. The ball goes high up in space. The player runs and catches the ball before it hits the ground. Which of the two ....
Step-by-Step Verified Solution
The short, direct answer is:
Both the player and the ball have the exact same displacement.
Step 1: Define Displacement
Displacement is the straight-line vector from the initial position to the final position.
It depends only on the start and end points—not on the path taken.
Displacement = Final position – Initial position (in vector form)
Step 2: Analyze the Ball
- Initial position: The point where the bat hits the ball (say, point P).
- Final position: The point where the player catches the ball (say, point Q).
- Path: The ball travels a high, curved parabolic trajectory through the air.
- Displacement of the ball: Straight line from P to Q.
Step 3: Analyze the Player
- Initial position: The player starts at the same point P (where he hit the ball).
- Final position: The player runs and catches the ball at point Q.
- Path: The player runs along the ground (a curved or straight path, depending on his route).
- Displacement of the player: Straight line from P to Q.
Step 4: Compare the Two Displacements
Quantity | Ball | Player |
Initial position | P (where hit) | P (where hit) |
Final position | Q (where caught) | Q (where caught) |
Displacement | Vector from P to Q | Vector from P to Q |
Since both start at P and both end at Q, their displacements are identical—same magnitude, same direction.
Displacement of the ball = Displacement of the player
Step 5: Common Misconception
Many students might say the ball has greater displacement because it traveled a longer, curved path. But that is distance, not displacement.
- Distance (path length) for the ball = Length of the parabolic arc (large).
- Distance for the player = Length of the running path on the ground (smaller, but could be curved).
- Displacement for both = Straight-line distance between P and Q (same for both).
So the player and the ball have different distances, but equal displacements.
Step 6: What if the player catches the ball at a different point?
If the player catches the ball at a point Q' that is not directly below the ball's landing point (i.e., he runs to a different spot), then:
- Ball's final position = where it lands (say, R).
- Player's final position = where he catches it (say, Q').
In that case, their displacements would be different because their final positions are different.
But the question states: "The player runs and catches the ball" — this implies he catches it at the point where the ball comes down, so both final positions are the same (Q).
Quick Summary Table
Aspect | Ball | Player | Equal? |
Initial position | P | P | ✅ Same |
Final position | Q | Q | ✅ Same |
Displacement (vector from P to Q) | d | d | ✅ Equal |
Distance (path length) | Long (parabolic arc) | Shorter (ground path) | ❌ Different |
Final Answer
Both the player and the ball have the same displacement.
Because displacement depends only on the initial and final positions, and both start at the same point (where the ball was hit) and end at the same point (where the ball is caught).
The ball travels a much longer distance (the curved path through the air), but its displacement is identical to the player's straight-line vector from start to catch point.