Important Relative Motion Formulas For JEE
Relative motion is a fundamental concept in physics that deals with the motion of one object with respect to another. It is a crucial topic in the Joint Entrance Examination (JEE) and other competitive exams. Understanding relative motion is essential for solving problems related to dynamics, kinematics, and other areas of physics. In this article, we will discuss some important relative motion formulas that will help you excel in your JEE preparation.
Relative Velocity:
Relative velocity refers to the velocity of one object as observed from the frame of reference of another object. It is a vector quantity and is crucial in solving problems involving moving objects. The formula for relative velocity (V_rel) of object A with respect to object B is given by:
Relative Displacement:
Relative displacement is the change in the position of one object as observed from the frame of reference of another object. It is also a vector quantity and is calculated by subtracting the initial position of the reference object from the final position of the moving object. The formula for relative displacement (Δr) of object A with respect to object B is given by:
Relative Acceleration:
Relative acceleration is the change in the velocity of one object as observed from the frame of reference of another object. It is calculated by subtracting the acceleration of the reference object from the acceleration of the moving object. The formula for relative acceleration (Δa) of object A with respect to object B is given by:
Relative Speed:
Relative speed is the magnitude of the relative velocity between two objects. It is a scalar quantity and can be found by taking the magnitude of the relative velocity vector. The formula for relative speed (Vrel) is given by:
Where:
Vrel is the relative speed between objects A and B.
VA is the velocity of object A.
VB is the velocity of object B.
Relative Motion in Two Dimensions:
In many physics problems, objects move in two dimensions, and it's essential to apply relative motion concepts accordingly. In such cases, you can break down the motion into horizontal and vertical components and use the relative motion formulas separately for each component.
Relative Motion in River Flow
Let's examine a scenario where a man is swimming in a river, moving with a velocity VMR relative to the river, at an angle θ with the direction of the river's flow. The river itself has a velocity VR. We can analyze this situation from the perspectives of two different observers: Observer 1, who is stationed on the ground, and Observer 2, who is situated on a raft floating along with the river's current.
From the viewpoint of Observer 2, who is on the raft moving with the river, the man's motion appears to mirror that of the river. In other words, the man will be seen as moving at an angle θ with respect to the river's flow by Observer 2.
On the other hand, for Observer 1, who is stationary on the ground, the velocity of the river must be considered in addition to the swimmer's velocity relative to the river. In this case, the swimmer's apparent velocity, denoted as VM, is calculated as VM = VMR + VR. Consequently, from Observer 1's perspective, the swimmer will appear to be moving at an angle θ’ with respect to the river's flow.
Drift
Drift refers to the displacement of an individual in the same direction as the river's current. In the diagram provided, 'x' represents the extent of this drift.
Optimal River Crossing Time
To minimize the time required to traverse the river, it is most efficient for the person to swim directly perpendicular to the river's current. The minimum time, denoted as Tmin, is given by Tmin = d/VMR.
Optimal River Crossing Path with Minimal Drift
Achieving the lowest possible drift implies that the individual's displacement in the direction of the river's flow is zero. In this particular scenario, when observed from the ground, the person swims directly perpendicular to the river's current, following the shortest path. To achieve minimal drift, the person needs to swim at an angle Φ relative to the perpendicular line in a backward direction. This angle is determined by the equation sin Φ = VR/VMR.
Time required to cross the river along the shortest path can be calculated as:
t = d/VMR cos Φ
Wind Airplane Problem
The "Wind-Airplane" problem is a classic physics problem often used to illustrate the concept of vector addition. It involves an airplane flying through the air with wind affecting its motion.
Here
Rain Problem
When raindrops are falling directly downward with a velocity VR while an observer is simultaneously moving horizontally with a velocity VM, the resulting velocity of the rain relative to the observer can be determined.
Understanding relative motion is crucial for solving a wide range of physics problems, especially in competitive exams like JEE. The formulas discussed in this article provide a solid foundation for tackling relative motion problems efficiently. By mastering these formulas and practicing various scenarios, you'll be well-prepared to excel in your JEE physics examination.
Important Relative Motion Formulas For JEE FAQs
Q1. What is relative motion, and why is it important for JEE?
Ans. Relative motion deals with the motion of one object as observed from the frame of reference of another moving object. It is vital for JEE as it forms the basis for solving problems in kinematics, dynamics, and various other physics concepts.
Q2. What is relative velocity, and how is it calculated?
Ans. Relative velocity is the velocity of one object as observed from the perspective of another object. It is calculated by subtracting the velocity of the second object from the velocity of the first object. In formula form:
Vrel=VA−VB.
Q3. What is relative displacement, and how is it different from absolute displacement?
Ans. Relative displacement is the change in position of one object as observed from the frame of reference of another object. It's calculated by subtracting the initial position of the reference object from the final position of the moving object. Relative displacement differs from absolute displacement because it considers the change in position from a specific viewpoint.
Q4. What is the significance of relative acceleration?
Ans. Relative acceleration represents the change in velocity of one object as observed from the perspective of another object. It helps in understanding how the relative motion between two objects is changing over time.
Q5. What is the formula for relative speed, and when is it useful?
Ans. Relative speed is the magnitude of the relative velocity between two objects. It is calculated by taking the absolute value of the relative velocity vector.
∣. Relative speed is useful when determining how fast one object is moving with respect to another.
