A ship moves along equator to the east with velocity 30km/hr. The south-eastern wind blows at an angle of 60° to equator with velocity 15 km/hr. Find the wind velocity relative to ship and angle between the equator and the wind direction in reference frame fixed to the ship. from Physics Motion in A Plane Class 11 Manipur Board
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A ship moves along equator to the east with velocity 30km/hr. The south-eastern wind blows at an angle of 60° to equator with velocity 15 km/hr. Find the wind velocity relative to ship and angle between the equator and the wind direction in reference frame fixed to the ship.

Velocity of the ship = 30 km/hr

Velocity of south-eastern wind = 15 km/hr

The velocity of wind relative to ship is given by,
stack straight v subscript straight t with rightwards harpoon with barb upwards on top space equals space v with rightwards harpoon with barb upwards on top subscript w space minus space v with rightwards harpoon with barb upwards on top subscript s



Here, we have

Angle space between space stack straight v subscript straight w with rightwards harpoon with barb upwards on top space and space straight v with rightwards harpoon with barb upwards on top subscript straight s comma space straight theta space equals space 120 to the power of 0

Angle space between space straight v with rightwards harpoon with barb upwards on top subscript straight w space and space minus straight v with rightwards harpoon with barb upwards on top subscript straight s space equals space 60 to the power of straight o

Now the magnitude of relative velocity of wind relative to ship is, 

open vertical bar v with rightwards harpoon with barb upwards on top subscript r close vertical bar space equals space open vertical bar v with rightwards harpoon with barb upwards on top subscript w minus v with rightwards harpoon with barb upwards on top subscript s close vertical bar space equals space open vertical bar v with rightwards harpoon with barb upwards on top subscript w plus left parenthesis negative v with rightwards harpoon with barb upwards on top subscript s right parenthesis close vertical bar space

space space space space space space space space space equals square root of open vertical bar v with rightwards harpoon with barb upwards on top subscript w close vertical bar squared plus open vertical bar negative v with rightwards harpoon with barb upwards on top subscript s close vertical bar squared plus 2 open vertical bar v with rightwards harpoon with barb upwards on top subscript w close vertical bar open vertical bar negative v with rightwards harpoon with barb upwards on top subscript s close vertical bar cos space left parenthesis 60 right parenthesis end root space

space space space space space space space space space equals space square root of 15 squared plus 30 squared plus 2 cross times 15 cross times 30 cross times left parenthesis 5.0 right parenthesis end root space equals space square root of 1575 space

rightwards double arrow space space open vertical bar v with rightwards harpoon with barb upwards on top subscript w minus v with rightwards harpoon with barb upwards on top subscript s close vertical bar space equals space 36.7 space m divided by s

The space angle space that space the space reltive space velocity space makes space with space minus straight v with rightwards harpoon with barb upwards on top subscript straight s space is comma space

space tan space alpha space equals space fraction numerator open vertical bar v with rightwards harpoon with barb upwards on top subscript w close vertical bar sin space 60 to the power of o over denominator open vertical bar negative v with rightwards harpoon with barb upwards on top subscript s close vertical bar plus open vertical bar v with rightwards harpoon with barb upwards on top subscript w close vertical bar c o s space left parenthesis 60 end fraction space equals space fraction numerator 15 cross times open parentheses begin display style bevelled fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses over denominator 30 plus 15 left parenthesis 0.5 right parenthesis end fraction space equals space fraction numerator square root of 3 over denominator 5 end fraction

rightwards double arrow space space space alpha space equals space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 5 end fraction close parentheses space equals space 19.1
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