Question

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After driving around and undergoing a displacement of Δrx=24.1 kmΔrx=24.1 km and Δry=−15.5 km,Δry=−15.5 km, a driver finds herself at position r2x=−39.7 kmr2x=−39.7 km and r2y=15.9 km.r2y=15.9 km. What were the components of the driver's initial position vector, r1xr1x and r1y,r1y, in kilometers?

r1x=r1x=

km

r1y=r1y=

km

Answer 1

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If Δx = 5m this means the x value has increased by 5m.
If Δx = -5m, this means the x value has reduced by 5m.
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So x₂ = x₁ + Δx

It follows that:
Δx = x₂ - x₁
x₁ = x₂ - Δx


r1x = r2x - Δrx
= (-39.7) - (24.1)
= -63.8 km

r1y = r2y - Δry
. = (15.9) - (-15.5)
= 31.4 km

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