Question

A man is swimming in a lake in a direction of 30° East of North with a speed of 5 kmh and a cycists
going on a road along the lake shore towards East at a speed of 10 kmh. In what directon and with
what speed would the man appear to swim to the cycist​

Answer 1

Answer:

5√3  km /Hr

60° West of North

Explanation:

A man is swimming in a lake in a direction of 30° East of North with a speed of 5 kmh and a cycists  going on a road along the lake shore towards East at a speed of 10 kmh. In what directon and with  what speed would the man appear to swim to the cyclist​

Swimmer speed 5 km/h  30° East Of North

Swimmer  speed towards North = 5 Cos30° = 5√3/2  km/hr

Swimmer speed towards East = 5 Sin30° = 5/2  km/hr

Cyclist Speed = 10 km/h  East  ( north = 0)

the man appear to swim to the cyclist​ =  Speed of Swimmer - Speed of cyclist

= 5√3/2  km/hr North  &  ( 5/2  - 10)  km/Hr East

=   5√3/2  km/hr North & 15/2 km hr West   ( -East = West)

Resultant speed = √(5√3/2)² + (15/2)²  = 5√3  km /Hr

Angle = Tanα = (15/2)/(5√3/2) = √3

=> α = 60°

60° West of North

the man appear to swim to the cycist​ 5√3  km /Hr 60° West of North