Answer to Question #205383 in Physics for Sphilile

Question

A chimpanzee sitting against his favourite tree get up and walk 45 m due north and 22 m due west to reach a termite mound,where he eats lunch.What is the shortest distance between the tree and the termite mound, and what angle does the shortest distance make with respect to due north? A.6,9 m;105° B.10 m;10° C.50 m;26.1° D.0.08 m;90° E.22 m;45°

Answer 1

We can find the shortest distance between the tree and the termite mound from the Pythagorean theorem:

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{(22\ m)^2+(45\ m)^2}=50\ m.$$

We can find the angle from the geometry:

$$cos\theta=\dfrac{d_y}{d},$$ $$\theta=cos^{-1}(\dfrac{d_y}{d})=cos^{-1}(\dfrac{45\ m}{50\ m})=26.1^{\circ}.$$

Therefore, the correct answer is (C) 50 m; $26.1^{\circ}$(with respect to due north).