Question

1. an antelope trots 40m east, then turns at a 45° angle and trots 70m southeast. which gives the correct solution for the magnitude of the total displacement?

Explanation:

Step1: Resolve the second - displacement vector into components

The second displacement of $d_2 = 70m$ at an angle of $45^{\circ}$ south - east. In the x - direction (east - west), $d_{2x}=70\cos45^{\circ}$ and in the y - direction (north - south), $d_{2y}=- 70\sin45^{\circ}$ (negative because it is in the south direction).
$d_{2x}=70\times\frac{\sqrt{2}}{2}\approx70\times0.707 = 49.49m$
$d_{2y}=-70\times\frac{\sqrt{2}}{2}\approx - 49.49m$
The first displacement is $d_1 = 40m$ in the x - direction (east).

Step2: Calculate the total x - component of the displacement

The total x - component of the displacement $D_x=d_1 + d_{2x}=40 + 49.49=89.49m$

Step3: Calculate the total y - component of the displacement

The total y - component of the displacement $D_y=d_{2y}=-49.49m$

Step4: Calculate the magnitude of the total displacement

The magnitude of the displacement vector $\vec{D}$ is given by $D=\sqrt{D_x^{2}+D_y^{2}}$.
$D=\sqrt{(89.49)^{2}+(-49.49)^{2}}=\sqrt{8008.46 + 2449.26}=\sqrt{10457.72}\approx102.26m$

Answer:

Approximately $102m$