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QPage 48-49: Q9: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q9 Solution: A food packet is dropped from a plane going at an altitude of…

A food packet is dropped from a plane going at an altitude of 100 m. What is the path of the packet as seen from ....


Step-by-Step Verified Solution

Let's break it down step-by-step.

Step 1: Setup of the Problem

  1. A plane is flying horizontally at a constant speed (say, v₀) at an altitude of 100 m.
  2. A food packet is dropped from the plane (released from rest relative to the plane).
  3. Ignore air resistance (assume free fall under gravity only).

Step 2: Path as seen from the plane

From the pilot's perspective (or any observer moving with the plane):

  1. The plane is at rest in its own frame.
  2. When the packet is dropped, it has zero horizontal velocity relative to the plane.
  3. The packet simply falls straight down under gravity.

Path observed: A vertical straight line downward.

✅ Answer: The path is a straight vertical line from the plane to the ground.

Step 3: Path as seen from the ground

From the ground observer (stationary relative to Earth):

  1. The plane is moving horizontally at speed v₀.
  2. When the packet is dropped, it retains the horizontal velocity v₀ of the plane (since there is no horizontal force).
  3. It also has a downward acceleration g due to gravity.
  4. The motion is a combination of:
  5. Uniform horizontal motion (constant v₀)
  6. Uniformly accelerated vertical motion (under gravity)

This is the classic projectile motion.

Path observed: A parabolic trajectory (half of a parabola) from the release point to the ground.

✅ Answer: The path is a parabola (specifically, a concave-downward parabolic arc).

Step 4: If someone asks, "what is the actual path?"

This is the deepest part of the question. Here is the answer:

There is no single "actual" or "absolute" path. Motion is relative—it depends on the frame of reference of the observer.
  1. In the plane's frame, the path is a straight vertical line.
  2. In the ground frame, the path is a parabola.

Both are equally correct descriptions of the same physical event. There is no absolute "true" path; there are only paths relative to a chosen reference frame.

This is the essence of Galilean relativity:

"All motion is relative, and there is no privileged or absolute frame of reference."

Step 5: What if we add air resistance?

If air resistance is considered:

  1. From the plane: the packet would still fall more or less vertically, but may drift slightly backward depending on wind.
  2. From the ground: the path would be a distorted parabola (not a perfect mathematical parabola) because the horizontal velocity decreases due to drag.

But in the ideal case (no air resistance), the paths are exactly as described above.

Quick Summary Table


Observer

Path of the packet

From the plane

Straight vertical line (downward)

From the ground

Parabolic arc

"Actual" path

No single answer—path is frame-dependent. Both are equally valid.

Final Answer

From the plane: The packet appears to fall in a straight vertical line (since it has no horizontal velocity relative to the plane).
From the ground: The packet follows a parabolic path (projectile motion).
If someone asks for the "actual" path: The correct response is that there is no absolute path—motion is relative. The path depends on the observer's frame of reference, and both descriptions are equally correct.


All Questions in this Chapter

QP 49-50: Q1 QP 49-50: Q2 QP 49-50: Q3 QP 49-50: Q4 QP 49-50: Q5 QP 49-50: Q6 QP 49-50: Q7 QP 49-50: Q8 QP 49-50: Q9 QP 49-50: Q10 QP 49-50: Q11 QP 49-50: Q12 QP 49-50: Q13 QP 50-51: Q1 QP 50-51: Q2 QP 50-51: Q3 QP 50-51: Q4 QP 50-51: Q5 QP 50-51: Q6 QP 50-51: Q7 QP 50-51: Q8 QP 50-51: Q9 QP 50-51: Q10 QP 51-54: Q1 QP 51-54: Q2 QP 51-54: Q3.1 QP 51-54: Q3.2 QP 51-54: Q3.3 QP 51-54: Q3.4 QP 51-54: Q4.1 QP 51-54: Q4.2 QP 51-54: Q5 QP 51-54: Q6 QP 51-54: Q7 QP 51-54: Q8.1 QP 51-54: Q8.2 QP 51-54: Q8.3 QP 51-54: Q9.1 QP 51-54: Q9.2 QP 51-54: Q10 QP 51-54: Q11 QP 51-54: Q12 QP 51-54: Q13 QP 51-54: Q14 QP 51-54: Q15.1 QP 51-54: Q15.2 QP 51-54: Q15.3 QP 51-54: Q16 QP 51-54: Q17 QP 51-54: Q18.1 QP 51-54: Q18.2 QP 51-54: Q19 QP 51-54: Q20 QP 51-54: Q21 QP 51-54: Q22 QP 51-54: Q23.1 QP 51-54: Q23.2 QP 51-54: Q23.3 QP 51-54: Q24 QP 51-54: Q25.1 QP 51-54: Q25.2 QP 51-54: Q25.3 QP 51-54: Q26 QP 51-54: Q27 QP 51-54: Q28 QP 51-54: Q29 QP 51-54: Q30 QP 51-54: Q31 QP 51-54: Q32.1 QP 51-54: Q32.2 QP 51-54: Q32.3 QP 51-54: Q33.1 QP 51-54: Q33.2 QP 51-54: Q34 QP 51-54: Q35 QP 51-54: Q36 QP 51-54: Q37 QP 51-54: Q38 QP 51-54: Q39 QP 51-54: Q40 QP 51-54: Q41 QP 51-54: Q42 QP 51-54: Q43.1 QP 51-54: Q43.2 QP 51-54: Q44 QP 51-54: Q45 QP 51-54: Q46.1 QP 51-54: Q46.2 QP 51-54: Q47.1 QP 51-54: Q47.2 QP 51-54: Q48 QP 51-54: Q49.1 QP 51-54: Q49.2 QP 51-54: Q50 QP 51-54: Q51 QP 51-54: Q52 QPage 48-49: Q1 QPage 48-49: Q2 QPage 48-49: Q3 QPage 48-49: Q4 QPage 48-49: Q5 QPage 48-49: Q6 QPage 48-49: Q7 QPage 48-49: Q8 QPage 48-49: Q9 QPage 48-49: Q10.1 QPage 48-49: Q10.2 QPage 48-49: Q10.3 QPage 48-49: Q11 QPage 48-49: Q12 QPage 48-49: Q13 QPage 48-49: Q14

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