In this example we will solve a relative motion problem involving only two frame

Question

In this example we will solve a relative motion problem involving only two frames of reference. Suppose you are driving north on a straight two-lane road at a constant 84 km/h (Figure 1) . A truck traveling at a constant 108 km/happroaches you (in the other lane, fortunately). (a)What is the truck’s velocity relative to you? (b)What is your velocity with respect to the truck?

A) Suppose you and the truck are both traveling in the northbound lane. (Let’s assume the truck has recently passed you, so we don't need to worry about a collision.) If we continue to let north be the positive direction, what is the truck’s velocity relative to you? Express your answer in kilometers per hour to the nearest integer.

B) What is your velocity with respect to the truck? Express your answer in kilometers per hour to the nearest integer.

Explanation / Answer

if there are two objects A and B , moving with speed Va and Vb ,

then speed of A relative to B=Va-Vb

and speed of B relative to A=Vb-Va

given that your speed=84 km/hr

truck's speed=-108 km/hr (as it is moving in opposite direction)

a)

relative velocity of truck with respect to you=speed of truck- your speed=-108-84=-192 km/hr

hence truck is moving at 192 km/hr along south relative to you.

b) your speed relative to the truck =your speed-truck's speed=84-(-108)=192 km/hr, along north

c) now, the truck's speed=108 km/hr

truck's relative veloicty=truck's speed-your speed=108-84=24 km/hr, along north

d) your relative speed=your speed-truck's speed=84-108=-24 km/hr

i.e. 24 km/hr, along south.

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