Physics Tutor in Bhosale Nagar Pune – Relative Motion Projectile Question Explained by Kumar Sir
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If you are searching for a Physics Tutor in Bhosale Nagar Pune for IIT JEE, NEET, Class 11, Class 12, or advanced Physics numericals, then understanding projectile motion and relative motion becomes extremely important. Many students feel projectile motion is difficult because they try to memorize formulas instead of understanding the logic behind motion.
According to Kumar Sir, Physics becomes easy when students understand components properly.
The Question Discussed by Kumar Sir
Two stones are projected simultaneously.
First stone is projected with speed:
[
20\sqrt{3}\ \text{m/s}
]
at an angle of:
[
60^\circ
]
from horizontal.
The second stone is projected with speed:
[
20\ \text{m/s}
]
at angle:
[
30^\circ
]
The horizontal distance between them is:
[
20\ \text{m}
]
The question asks:
What will be the minimum separation between the two stones?
Step 1 – Resolve the Components
According to Kumar Sir, every projectile question starts with component breakdown.
For first particle:
Horizontal component:
20\sqrt{3}\cos60^\circ=10\sqrt{3}
Vertical component:
20\sqrt{3}\sin60^\circ=30
Now for second particle:
Horizontal component:
20\cos30^\circ=10\sqrt{3}
Vertical component:
20\sin30^\circ=10
The Most Important Observation
Now comes the real Physics.
Students usually start applying formulas immediately.
But Kumar Sir says:
“First observe the motion physically.”
Notice carefully:
Both particles have same horizontal velocity:
[
10\sqrt{3}\ \text{m/s}
]
That means horizontally they move together.
Relative horizontal velocity becomes:
[
0
]
Now think about vertical motion.
One particle moves upward faster than the other.
Their vertical separation changes with time.
Relative Motion Concept
In relative motion, minimum separation occurs when relative velocity becomes perpendicular to relative position.
But here an even simpler observation exists.
Since horizontal relative velocity is zero, the horizontal distance between them always remains:
[
20\ \text{m}
]
Therefore, they can never collide.
This is the key concept students usually miss.
Many students incorrectly think minimum separation becomes zero.
But collision is impossible because horizontal separation never changes.
Minimum Separation
Since horizontal distance remains fixed:
[
20\ \text{m}
]
Minimum possible distance cannot become smaller than 20 m.
At one instant, vertical separation may become zero.
At that moment:
[
\text{Minimum Separation}=20\ \text{m}
]
Final Answer
d_{\min}=20\text{ m}
How Kumar Sir Teaches Projectile Motion
According to Kumar Sir, projectile motion is one of the easiest chapters if students understand:
Components
Relative motion
Horizontal independence
Vertical independence
Physical visualization
Students are trained to:
Break vectors instantly
Visualize motion mentally
Avoid unnecessary formulas
Solve JEE numericals quickly
Handle NEET assertion questions
Why Students Like Kumar Sir’s Teaching
Students preparing for:
IIT JEE
NEET
AP Physics
Olympiads
Boards
prefer Kumar Sir because concepts are taught deeply.
Topics covered include:
Relative motion
Projectile motion
Kinematics
HC Verma
Advanced numericals
Graphical Physics
Multi-concept questions
Students learn not only formulas but actual Physics thinking.
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Relative Velocity – Complete Concept Explained by Kumar Sir
Relative velocity is one of the most important concepts in Physics, especially in kinematics, projectile motion, river boat problems, rain problems, and collision-based numericals. According to Kumar Sir, students often memorize formulas of relative velocity without understanding the actual meaning of motion. But real Physics begins when students start visualizing motion from different frames of reference.
Relative velocity simply means:
“How fast one object appears to move with respect to another object.”
This definition is extremely important.
Suppose two cars are moving on a road. One car is moving at 40 m/s and another at 30 m/s. A person sitting in one car does not observe the absolute velocity of the second car. Instead, he observes how fast the second car appears to move relative to him. That observed velocity is called relative velocity.
Mathematically, relative velocity is written as:
\vec{V}_{AB}=\vec{V}_A-\vec{V}_B
This means velocity of A relative to B equals velocity of A minus velocity of B.
According to Kumar Sir, the biggest mistake students make is forgetting the direction of vectors. Relative velocity is always a vector quantity. Therefore, direction is extremely important.
If two particles move in the same direction, then relative velocity becomes the difference of their velocities.
For example:
Car A moves at 50 m/s
Car B moves at 30 m/s
Then relative velocity becomes:
[
50 – 30 = 20 \text{ m/s}
]
This means one car appears to move at 20 m/s relative to the other.
Now suppose two cars move in opposite directions. Then relative velocity increases because velocities add up.
If:
Car A moves right at 40 m/s
Car B moves left at 20 m/s
Then relative velocity becomes:
[
40 + 20 = 60 \text{ m/s}
]
This is why trains moving in opposite directions cross each other very quickly.
According to Kumar Sir, relative velocity is not just a formula chapter. It is actually a change of observer.
This idea becomes very important in advanced Physics.
Suppose rain falls vertically downward. A standing person sees rain vertically. But a moving person sees rain coming at an angle. Why? Because the observer himself is moving. This is one of the most beautiful applications of relative velocity.
Similarly, in river boat problems:
Water has one velocity
Boat has another velocity
Actual motion becomes the vector sum of both.
Students often get confused in these questions because they try to solve everything algebraically. But Kumar Sir always says:
“First visualize motion physically.”
Relative velocity is heavily used in projectile motion also.
For example, when two particles are projected simultaneously, instead of analyzing both independently, we study motion of one particle relative to the other. This simplifies difficult IIT JEE problems tremendously.
In collision problems also, relative velocity becomes extremely important.
One golden rule is:
Relative velocity before collision equals negative of relative velocity after collision multiplied by coefficient of restitution.
This concept is frequently used in advanced mechanics.
Relative velocity is also used in:
Airplane and wind problems
River crossing
Rain man problems
Collision mechanics
Circular motion
Projectile motion
Satellite motion
Relative acceleration problems
According to Kumar Sir, students should always remember one key point:
“Motion depends on observer.”
This single statement explains the entire chapter of relative velocity beautifully.
A stationary object for one observer may appear moving for another observer. That is why relative velocity is one of the most conceptually powerful topics in Physics.
Students preparing for:
IIT JEE
NEET
AP Physics
Olympiads
Board examinations
must develop strong visualization skills in relative motion because this chapter builds the foundation for advanced mechanics and real-world Physics applications.
Three Particle Triangle Problems – Explained by Kumar Sir Using Relative Motion and Newtonian Logic
One of the most interesting problems in Physics and mathematics is when three particles or three persons start moving from the vertices of a triangle toward each other. These problems are very common in relative motion and are based on Newtonian logic, symmetry, and velocity concepts.
Suppose three persons are standing at the corners of an equilateral triangle. Each person starts running toward the next person with the same speed. For example:
Person A runs toward B
Person B runs toward C
Person C runs toward A
Now students usually get confused because they think the particles will move in straight lines. But actually, their direction continuously changes because every particle is chasing another moving particle.
According to Kumar Sir, the biggest idea in these questions is:
“The shape remains similar during the motion.”
If initially the particles form an equilateral triangle, then during the entire motion they continue forming a shrinking equilateral triangle.
This is the key observation.
Now let the side of the triangle be (a) and speed of each particle be (v).
The distance between any two particles decreases because each particle has a velocity component toward the other particle.
Using relative velocity logic, the effective speed with which the side decreases becomes:
v_{rel}=v\cos60^\circ+v\cos60^\circ=v
Why?
Because angle between velocity and side is (60^\circ).
Therefore, the side length decreases at speed (v).
Now if initial side length is (a), total time to meet becomes:
t=\frac{a}{v}
This is one of the most beautiful results.
Students often think complicated calculus is required, but symmetry and relative motion simplify the question tremendously.
Now another important concept is trajectory.
The path followed by each particle is not straight. It becomes a curved spiral-like path toward the center of the triangle.
According to Kumar Sir, these problems teach students three very important Physics ideas:
Relative velocity
Symmetry
Continuous change in direction
These concepts are heavily used later in:
Circular motion
Rotational dynamics
Electromagnetism
Orbital mechanics
The most important thing in such questions is visualization.
Students should mentally imagine:
How distance changes
Which direction velocity acts
How symmetry simplifies motion
That is why Kumar Sir always teaches students to think physically before applying formulas.