Lesson_Text_1.5 - 1 Lesson 1.5 Relative Velocity and...

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1 Lesson 1.5 Relative Velocity and Solving Problems in Projectile Motion 1 . Relative Velocity: All velocities are relative, it depends on the frame in which the measurement is made. For example if you are in a car traveling in the positive x direction at 20 m/s, a passenger sitting next to you will see you at rest while a person standing by the side of the road will measure your velocity as 20 m.s -1 i. A person in a car moving in the negative x direction at 15 m.s -1 will measure your velocity as 35 m.s -1 i. Yet another person in a car traveling in the positive x direction at 25 m/s will measure your velocity as –5 m.s -1 i! In this section you will develop the skills needed to measure the velocity of one object relative to another moving object. If two objects A and B are moving, the velocity of A relative to B is obtained by the following two steps. (i) Impose a velocity equal and opposite to that of B to both A and B. This will bring B to rest and give A two velocities, its own and the equal and opposite velocity of B imposed on it. (ii) Find the resultant of these two velocities of A. That will be the velocity of A relative to B To find the relative velocity of B with respect to A, bring A to rest by applying an equal and opposite velocity of A to both and find the resultant velocity of B. Example 1 : Car A has a velocity 10 m/s i and car B has a velocity 15 m/s i. Find (i) the velocity of A relative to B and (ii) the velocity of B relative to A. Solution: (i) Bring B to rest by imposing a velocity of –15 m.s -1 i to both A and B. A has now two velocities 10 m.s -1 i and –15 m.s -1 i. The resultant of these two velocities is given by 10 m.s -1 i – 15 m.s -1 i = -5 m.s -1 i . The velocity of A
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2 relative to B is –5 m.s -1 . This means that for people in car B, car A will appear to go backward with a velocity of 5 m.s -1 . (ii) Bring A to rest by imposing a velocity of –10 m.s -1 i to both A and B. B now has two velocities 15 m.s -1 i and –10 m.s -1 i. The resultant of these two velocities is given by 15 m.s -1 i – 10 m.s -1 i = 5 m.s -1 i . This means that for people in car A, car B will appear to go forward at 5 m.s -1 . Example 2 : Car A has a velocity of –20 m.s -1 j and car B has a velocity of 15 m.s -1 j. (i)What is the velocity of A relative to B? (ii) What is the velocity of B relative to A? Solution : (i) To find the velocity of A relative to B, bring B to rest by applying a velocity of –15 m.s -1 j to both A and B. A has now two velocities, -20 m.s -1 j and –15 m.s -1 j. The resultant of these two velocities is given by –20 m.s -1 j – 15 m.s -1 j = -35 m.s -1 j . (ii) To find the velocity of B relative to A, bring A to rest by applying a velocity of 20 m.s -1 j to both A and B. B has now two velocities 15 m.s -1 j and 20 m.s - 1 j. The resultant of these two velocities is given by 15 m.s -1 j + 20 m.s -1 j = 35 m.s -1 j. Example 3:
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Lesson_Text_1.5 - 1 Lesson 1.5 Relative Velocity and...

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