Relative Velocity in 2-D
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Relative Velocity in 2-D

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Questions and Answers

How long does it take for the bird to cross the train?

  • 15 s (correct)
  • 25 s
  • 20 s
  • 10 s

    • What is the relative speed of the two trains when they cross each other?

  • 108 km/h (correct)
  • 72 km/h
  • 36 km/h
  • 54 km/h

    • What speed must the scooterist maintain to overtake the bus in 100 seconds?

  • 25 m/s
  • 30 m/s
  • 15 m/s
  • 20 m/s (correct)

    • If both trains are 100m long, how long will it take for them to completely cross each other?

    <p>6.67 s</p> Signup and view all the answers

    What is the speed of the train moving north?

    <p>10 m/s</p> Signup and view all the answers

    What is the velocity of Pinki represented in the coordinate system?

    <p>(10, 0)</p> Signup and view all the answers

    What does the notation $v_{AP} = (-6, 0°)$ indicate?

    <p>Pinki is moving at a speed of 6 in the negative x-direction.</p> Signup and view all the answers

    If $v_{PR} = (6, 70°)$, what does the angle represent?

    <p>The direction of the velocity vector.</p> Signup and view all the answers

    How is the relationship between $v_{PR}$ and $v_{RP}$ defined?

    <p>They are opposite in direction.</p> Signup and view all the answers

    What is the significance of the negative sign in $x_{PR} = -x_{RP}$?

    <p>It shows that $v_{PR}$ is in the opposite direction to $v_{RP}$.</p> Signup and view all the answers

    What is the formula for calculating relative velocity between two objects A and B?

    <p>$V_{AB} = V_A - V_B$</p> Signup and view all the answers

    In Case 1, what is the calculated relative velocity $V_{AB}$ between objects A and B?

    <p>-5</p> Signup and view all the answers

    What is the result of the relative velocity $V_{AB}$ in Case 3?

    <p>0</p> Signup and view all the answers

    What is the resulting velocity when calculating $V_{AB}$ in Case 4?

    <p>30</p> Signup and view all the answers

    How do you convert 54 km/hr to meters per second?

    <p>15</p> Signup and view all the answers

    What is the relative speed of object A compared to object B?

    <p>5 m/s</p> Signup and view all the answers

    If the velocity of object B is $2(10 - 5)$, what is its value?

    <p>10 m/s</p> Signup and view all the answers

    How does an observer perceive their own motion when viewing other objects?

    <p>They feel at rest while observing other moving objects.</p> Signup and view all the answers

    What does a position-time graph illustrate?

    <p>The speed of an object relative to time.</p> Signup and view all the answers

    What is the significance of relative separation in motion analysis?

    <p>It indicates how close two objects are to each other.</p> Signup and view all the answers

    What is the equation for the time when two objects meet again?

    <p>$t = 2u + rac{1}{2}(a)t^2$</p> Signup and view all the answers

    If Ramlal accelerates at $2 m/s^2$ from rest, what is his initial velocity?

    <p>$0 m/s$</p> Signup and view all the answers

    What is the velocity of the bus in the scenario described?

    <p>$1 m/s$</p> Signup and view all the answers

    What distance does the bus cover when Ramlal catches up?

    <p>100 + vt</p> Signup and view all the answers

    What is the solution for the time variable t from the equation $0 = t^2 + 21t - 100$?

    <p>-4 seconds</p> Signup and view all the answers

    What is the speed of the third car moving in the opposite direction?

    <p>60 km/h</p> Signup and view all the answers

    How far does each of the first two cars travel before the third car meets them?

    <p>2 km</p> Signup and view all the answers

    What is the time taken by the third car to meet the first and second cars?

    <p>9 minutes</p> Signup and view all the answers

    What is the minimum velocity required for the man to catch the bus after 5 seconds?

    <p>10 m/s</p> Signup and view all the answers

    How long does the bus accelerate to reach its speed of 10 m/s?

    <p>5 seconds</p> Signup and view all the answers

    What is the formula for the time taken by Preeti to walk up a moving escalator?

    <p>T = S/(Vm + Vs)</p> Signup and view all the answers

    If Preeti's speed on foot is represented by Vm and the speed of the escalator by Vs, what is the combined time taken on the escalator moving upwards?

    <p>T = S/(Vm + Vs)</p> Signup and view all the answers

    What is the relationship between the times t1 and t2 for Preeti walking and using the moving escalator?

    <p>T = t1 * t2/(t1 + t2)</p> Signup and view all the answers

    According to the table of relative motion in medium under gravity, what is the speed of an object moving upwards after 1 second?

    <p>40 m/s</p> Signup and view all the answers

    What does the notation VBA = 20m/s represent in the context of relative motion?

    <p>Speed of A with respect to B</p> Signup and view all the answers

    What is the speed of the boat in still water?

    <p>8 km/h</p> Signup and view all the answers

    If a man is walking on a stationary escalator, how would you calculate the time taken to cover a distance S?

    <p>t = S / Vm</p> Signup and view all the answers

    What formula represents the time taken when a man is stationary on a moving escalator?

    <p>t = S / Vs</p> Signup and view all the answers

    When a man is moving with the escalator, what is the correct expression for the time taken to cover distance S?

    <p>t = S / (Vm + Vs)</p> Signup and view all the answers

    How long did the boat take to travel downstream 30 km?

    <p>3 hours</p> Signup and view all the answers

    What type of motion does a ball exhibit when it is in free fall under the influence of gravity?

    <p>Non-uniform motion</p> Signup and view all the answers

    What is the value of $V_{m/g}$ when a bus is at rest?

    <p>40</p> Signup and view all the answers

    If a ball is dropped from a height of 80m, what happens to its velocity as it falls?

    <p>It increases steadily</p> Signup and view all the answers

    When a man swims downstream in a moving river, what is the formula for his velocity relative to the ground?

    <p>$V_{m/g} = VR + Vo$</p> Signup and view all the answers

    When a ball is thrown upwards with an initial speed of 50m/s, what will happen to its motion over time?

    <p>It will decelerate until it stops and then falls down</p> Signup and view all the answers

    What will $V_{m/g}$ equal if a man is swimming upstream in a river flowing at 40?

    <p>$40 - Vm$</p> Signup and view all the answers

    At what time do the two balls (one dropped from 80m and one thrown upwards) meet?

    <p>3 seconds</p> Signup and view all the answers

    If the bus is moving at 40 and the person inside is also moving at 40, what is the velocity of the person relative to the ground?

    <p>40 + Vo</p> Signup and view all the answers

    What type of problem does the scenario of two balls meeting emphasize in physics?

    <p>Equations of motion</p> Signup and view all the answers

    What effect does the river's flow have when a man is not swimming?

    <p>It results in a velocity of VR.</p> Signup and view all the answers

    Study Notes

    Relative Velocity in 2-D

    • Relative velocity concepts include ( V_{AB} = V_A - V_B ) and ( x_{AB} = x_B - x_A ).
    • Cases illustrate the computation of relative speeds under various scenarios.
    • Conversion for speed: ( 54 \text{ km/hr} = 15 \text{ m/s} ).

    Case Examples

    • Problem 1: A train travels North at 10 m/s, a bird South at 5 m/s. The time for the bird to cross the train is 15 seconds.
    • Problem 2: Two trains, each 100m long, moving parallel at 72 km/h and 36 km/h will take approximately 6.67 seconds to cross each other.
    • Problem 3: A bus travels at 10 m/s; a scooterist aims to overtake it in 100 seconds. The required speed of the scooterist is 20 m/s.

    Position-Time Graph and Comments

    • Velocity comparison: ( V_{pa} = 10 - 5 = 5 \text{ m/s} ) and ( V_{pb} = 2(10 - 5) = 10 \text{ m/s} ).

    Velocity and Relative Motion Problems

    • Meeting Time Equation: To find when two objects meet, use ( t = 2u + \frac{1}{2}at^2 ).
    • Ramlal's Catch-Up: For a bus moving at 1 m/s and Ramlal accelerating at 2 m/s², the equation ( ut + \frac{1}{2}at^2 = 100 + vt ) leads to finding non-negative time for catching up.

    Relative Motion of Cars

    • Two cars moving in the same direction with 30 km/h speeds, separated by 5 km, along with a third car moving opposite, yields the third car's speed as 60 km/h.

    Minimum Velocity Calculation

    • For a man catching a bus that accelerates from rest at 2 m/s² over 50m, required velocity to match the bus after 5 seconds is 10 m/s.

    Moving Frames of Reference

    • Situations illustrate how velocities transform in different frames, such as a moving bus, affecting observed speeds.

    Motion in Water Scenarios

    • A boat travels downstream 30 km in 3 hours, upstream in 5 hours, leading to a boat speed of 8 km/h in still water through derived equations.

    Escalator Motion

    • Three different scenarios for a man walking on an escalator demonstrate time calculations depending on whether the escalator is stationary or moving.

    Motion Under Gravity

    • In free fall, an object's motion is non-uniform due to variable acceleration instigated by gravity.

    Ball Drop Problem

    • A dropped ball from 80m meets an upward-thrown ball at approximately 3 seconds based on calculated values, demonstrating combined motion dynamics.

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    Quiz Team

    Description

    This quiz covers the concept of relative velocity in two dimensions, focusing on vector representation and directional components. Students will analyze velocities of different objects and their interactions. Ideal for physics students exploring kinematics.

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