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A plane travels north at 500 mph for 3hrs from Long Beach, CA to Portland, Oregon (non-stop).The plane after landing has to travel east from Portland, Oregon to New York at 547mph for 5hrs(non-stop). Find the displacement vector (resultant vector) of the plane. (3 sig figs and inscientific notation)

Question

A plane travels north at 500 mph for 3hrs from Long Beach, CA to Portland, Oregon (non-stop).The plane after landing has to travel east from Portland, Oregon to New York at 547mph for 5hrs(non-stop). Find the displacement vector (resultant vector) of the plane. (3 sig figs and inscientific notation)

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Solution

To find the displacement vector, we first need to calculate the displacement in each direction (north and east) separately.

  1. Calculate the displacement in the north direction: The plane travels north at 500 mph for 3 hours. So, the displacement in the north direction is speed * time = 500 mph * 3 hours = 1500 miles.

  2. Calculate the displacement in the east direction: The plane travels east at 547 mph for 5 hours. So, the displacement in the east direction is speed * time = 547 mph * 5 hours = 2735 miles.

  3. Now, we can represent these displacements as vectors. Let's represent the north direction as the y-axis and the east direction as the x-axis. So, the displacement vector in the north direction is (0, 1500) and in the east direction is (2735, 0).

  4. The resultant vector (displacement vector of the plane) is the sum of these two vectors. So, we add the corresponding components of the vectors: (0 + 2735, 1500 + 0) = (2735, 1500).

  5. In scientific notation (to 3 significant figures), this is (2.74 x 10^3, 1.50 x 10^3).

So, the displacement vector of the plane is (2.74 x 10^3, 1.50 x 10^3) miles.

This problem has been solved

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