Question

A motor cyclist is riding north in still air at 20km/h.if the wind starts blowing westward with a velocity of 45.8km/h.find the appreant velocity with which the motor cyclist moves time it takes to cover 100km and it's direction of motion.

Answer 1

The Motercyclist speed in north direction = 20 km/ hr

Velocity of wind is 45.8 km/hr in west direction.


so the actual velocity of the motor cyclist will be the vector sum of its own velocity and the velocity of wind.
As wind is blowing in a direction such that the angle between the velocities is 90o

so using the formula for vector addition we see:

R2 = A2 + B2  +2ABcos∅as ∅ = 90oso, R2 = A2 + B2assuming A = velocity of motorcyclist B = velocity of windwe get ,the Resultant velocity to be R = 202+45.82−−−−−−−−−√R = 400 + 2097.64−−−−−−−−−−−−√R = 2497.64−−−−−−−√so the net velocity will be  = 49.97 km/hr

part 2

Time to take 100 km,

Time taken  = 100/49.97 = 2 hours.

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Answer 2

The Motercyclist speed in north direction = 20 km/ hr

Velocity of wind is 45.8 km/hr in west direction.


so the actual velocity of the motor cyclist will be the vector sum of its own velocity and the velocity of wind.
As wind is blowing in a direction such that the angle between the velocities is 90o

so using the formula for vector addition we see:

R^2 = A^2 + B^2  +2ABcos∅

as ∅ = 90°

so, 

R^2 = A^2 + B^2

assuming 

A = velocity of motorcyclist

 B = velocity of wind

we get ,the Resultant velocity to be

 R = √20^2+{45.8}^2

R = √400 + 2097.64
R = √2497.64

so the net velocity will be  = 49.97 km/hr

part 2

Time to take 100 km,

Time taken  = 100/49.97 = 2 hours.