Question

figure 1 shows a map of olivias trip to a coffee shop. she gets on her bike at loomis and then rides south 0.9mi to broadway. she turns east onto broadway, rides 0.8 mi to where broadway turns, and then continues another 1.6mi to the shop. part a what is the magnitude of the total displacement of her trip? express your answer in miles. d = mi incorrect; try again; 5 attempts remaining it appears that you have incorrectly determined the y - component of displacement. note that olivia moves downward in the first part of her trip, but she moves upward in the last part

Explanation:

Step1: Determine the horizontal and vertical components

The horizontal (east - west) displacement $x = 0.8+1.6=2.4$ mi (east - direction is positive). The vertical (north - south) displacement $y=- 0.9$ mi (south - direction is negative and assume no upward movement in the vertical direction in other parts of the journey as per the description).

Step2: Use the Pythagorean theorem

The magnitude of the displacement $d$ is given by $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 2.4$ mi and $y=-0.9$ mi into the formula: $d=\sqrt{(2.4)^{2}+(- 0.9)^{2}}=\sqrt{5.76 + 0.81}=\sqrt{6.57}\approx2.56$ mi.

Answer:

$2.56$