Grade 11Mechanics

A man is swimming in a lake in a direction of 30° East of North with a speed of 5 km/hr and a cyclist isgoing on a road along the lake shore towards East at a speed of 10 km/hr. In what direction and withwhat speed would the man appear to swim to the cyclist.

Aditya Maurya

9 Years agoGrade 11

2 Answers

Vikas TU

9 Years ago

Speed of Man = 5 km/hr

Speed of cyclist = 10 km/hr

Angle = 30°

Relative speed of man with cyclist

= √(10²+ 5²+2*10*5* cos 60

√100+25+50
√175 = 5√7 m/sec

And the direction of man from the cyclist

Ѳ =( 5 sin 60)/(10+5cos60)

= (5√3/2)/ (10+5/2)

= (2.5√3)/12.5

= √3/5

= 1.732/5 = 0.346

Ѳ = tan^-1(0.346)

= 19.1^o

Nishtha

7 Years ago

Speed of man =5km/hr

Speed of cyclist=100km/hr

By using vectors

Angle with the horizontal is 120 degree

By applying relative motion

Speed of man w.r. t cyclist=

√(100+25-2*10*5cos60)=5√3 m/sec

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A man is swimming in a lake in a direction of 30° East of North with a speed of 5 km/hr and a cyclist isgoing on a road along the lake shore towards East at a speed of 10 km/hr. In what direction and withwhat speed would the man appear to swim to the cyclist.

Aditya Maurya

2 Answers

Vikas TU

Nishtha

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