Question

While vacationing in the mountains you do some hiking. In the morning, your displacement is S⃗ morning= (2200 m , east) + (4000 m north) + (200 m , vertical). After lunch, your displacement is S⃗ afternoon= (1600 m , west) + (2900 m , north) - (300 m , vertical).

Part A

At the end of the hike, how much higher or lower are you compared to your starting point?

Express your answer with the appropriate units

Part B

What is the magnitude of your net displacement for the day?

Express your answer with the appropriate units.

Answer 1

We know that East = +i, West = -i, North = +j, South = -j, Vertical upward = +k, Vertical downward = -k, So

Part A.

In the morning, you moved +200 m, Vertical direction, then After lunch you moved -300 m in vertical direction, So

Your net displacement in vertical direction was

d_z = + 200 m - |-300 m| = - 100 m

So At the end of the hike you were 100 m lower compared to your starting point

Use negative sign because you are at lower position compared to starting point.

d_z = -100 m

Part B.

Morning displacement = d_m = 2200 m, east + 4000 m north + 200 m , vertical

d_m = 2200 i + 4000 j + 200 k

After lunch displacement = d_a = 1600 m, west + 2900 m, north - 300 m, Vertical

d_a = -1600 i + 2900 j - 300 k

So Net displacement will be:

d = d_a + d_m

d = (2200 i + 4000 j + 200 k) + (-1600 i + 2900 j - 300 k)

d = 600 i + 6900 j - 100 k

Magnitude of displacement will be:

|d| = sqrt (600^2 + 6900^2 + (-100)^2)

|d| = 6926.76 m

|d| = 6930 m

Let me know if you've any query.