While John is traveling along a straight interstate highway, he notices that the mile marker reads 243 km. John travels until he reaches the 143 km marker and then retraces his path to the 163 km marker. What is John's resultant displacement from the 243 km marker? Answer in units of km.

Question

Mathematics

Ricky

2 January, 08:26

While John is traveling along a straight interstate highway, he notices that the mile marker reads 243 km. John travels until he reaches the 143 km marker and then retraces his path to the 163 km marker. What is John's resultant displacement from the 243 km marker? Answer in units of km.

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Answers (1)

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Sydnee Robles · Answer 1

The displacement is: - 80 i

Step-by-step explanation:

In order to answer the question, you have to apply the displacement formula, which is:

ΔX = Xf-Xi

Where ΔX is the displacement, Xf is the final position and Xi is the initial position. The formula represents the change in the position of an object from the origin.

Let the origin be in 0 km, with the x-axis positive to te right.

Notice that the displacement is a vector. The positions are:

Xf=163 km (i)

Xi = 243 km (i)

Because John starts in 243 km and finishes in 163 km.

Where i is the unit vector in the x direction.

Therefore:

ΔX = 163 i - 243 i

Solving:

ΔX = - 80 i

Notice that for calculating the displacement you just need the initial and final position. It doesn't depend on the distance traveled.