Question

Tom and Jerry start at the same location. Tom is travelling due east at a velocity of 5 m/hr. Jerry is travelling due northwest at a velocity of 6 m/hr. After 1 hour, how fast is the distance between them changing

Answer 1

Answer:

The distance between them is changing at the speed of 10.16 m/hr

Explanation:

Consider the sketch attached below.

The question is simply asking to calculate the resultant of the two velocities.

To get the angle between them, we simply use the coordinates of the two vectors to determine the angle between them.  

90 + 45 = 135°

from the cosine rule we have

$c^{2}$ = $a^{2}$ + $b^{2}$ - 2abcosθ

$c^{2}$ = $6^{2}$ +$5^{2}$ - 2 ×6×5×cos 135

$c^{2}$ = 103.426

c = $\sqrt{103.426}$

c = 10.17 m/hr