Answer:
The distance between the man and woman is changing at the rate of 1.5 m/sec.
Step-by-step explanation:
Speed = [tex]\frac{distance}{time}[/tex]
⇒ distance = speed x time
After 35 minutes (2100 seconds) ,
the man has walked a distance = 1.3 x 2100
= 2730 m
After 35 minutes, the woman has walked a distance = 1.6 x 2100
= 3360 m
The sketch of the displacement of the man and woman forms a triangle with an included angle. Applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos θ
= [tex]3360^{2}[/tex] + [tex]2730^{2}[/tex] - 2 x 3360 x 2730 x Cos [tex]60^{o}[/tex]
= 11289600 + 7452900 - 18345600(0.5)
= 18742500 - 9172800
= 9569700
c = [tex]\sqrt{9569700}[/tex]
= 3093.5 m
The distance between the man and woman at 35 minutes is 3093.5 m.
The distance between the man and woman is changing at the rate = [tex]\frac{3093.5}{2100}[/tex]
= 1.4731
= 1.5 m/sec
The distance between the man and woman is changing at the rate of 1.5 m/sec.
