Question

1. an antelope runs 40m east, then turns at a 45° angle and runs 70m southeast. which choice gives the correct solution for the magnitude of the total displacement? clear all r² = 40² + 70² r² = 40² + 70² - 2(40)(70)cos(135) r² = 40² + 70² - 2(40)(70)cos(45) r² = 70² - 40²

Explanation:

Step1: Identify the problem as vector - addition

We have two displacements and need to find the magnitude of the resultant displacement. We use the law of cosines for vectors.

Step2: Recall the law of cosines for vectors

If two vectors $\vec{A}$ and $\vec{B}$ with magnitudes $A$ and $B$ and the angle $\theta$ between them, the magnitude $R$ of the resultant vector $\vec{R}=\vec{A}+\vec{B}$ is given by $R^{2}=A^{2}+B^{2}-2AB\cos\theta$. Here $A = 40m$, $B = 70m$, and $\theta=135^{\circ}$ (since the direction of the second - displacement relative to the first forms an angle of $135^{\circ}$).

Step3: Substitute the values

Substitute $A = 40$, $B = 70$, and $\theta = 135^{\circ}$ into the law - of - cosines formula. So $R^{2}=40^{2}+70^{2}-2(40)(70)\cos(135^{\circ})$.

Answer:

$R^{2}=40^{2}+70^{2}-2(40)(70)\cos(135^{\circ})$