Question 89: Motion in 2D & Vectors

Question

A butterfly is flying with a velocity $$4\sqrt 2 $$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

Accepted Answer

The given situation can be represented as
In the above figure, v
1
is the speed of wind and v
21
is the speed of butterfly with respect to wind.
So, v
21
can be given as
$${v_{21}} = 4\sqrt 2 \cos 45^\circ \widehat i + 4\sqrt 2 \sin 45^\circ \widehat j$$
$$ = 4\sqrt 2  	imes {1 \over {\sqrt 2 }}\widehat i + 4\sqrt 2  	imes {1 \over {\sqrt 2 }}\widehat j = 4\widehat i + 4\widehat j$$
and v
1
can be given as
$${v_1} =  - \widehat j$$
$$	herefore$$ Velocity of butterfly can be given as
$${v_2} = {v_1} + {v_{21}} = 4\widehat i + 4\widehat j - \widehat j = 4\widehat i + 3\widehat j$$
$$	herefore$$ Displacement of butterfly, $$D = {v_2} 	imes t$$
$$ = (4\widehat i + 3\widehat j) 	imes 3 = 12\widehat i + 9\widehat j$$
$$	herefore$$ Magnitude of displacement, $$\left| D ight| = \sqrt {{{12}^2} + {9^2}}  = 15$$ m

Answer

$$12\sqrt 2 $$ m

Answer

20 m

Answer

3 m

Answer

15 m

Motion in 2D & Vectors

A butterfly is flying with a velocity $4\sqrt 2 $ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

Choose the correct answer: