Question 91: Motion in 2D & Vectors

Question

A mosquito is moving with a velocity $$\overrightarrow v  = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?

Accepted Answer

$$\overrightarrow v  = (0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k)$$ m/s
At t = 2 s
$$\overrightarrow v  = (2\widehat i + 6\widehat j + 9\widehat k)$$
Direction cosine along y-axis,
$$cos	heta  = {{(v.\widehat j)} \over {\sqrt {{9^2} + {6^2} + {2^2}} }} = {6 \over {\sqrt {121} }} = {6 \over {11}}$$
$$ 	herefore $$ $$\sin 	heta  = {{\sqrt {85} } \over {11}}$$
and $$	an 	heta  = {{\sqrt {85} } \over 6}$$
$$ 	herefore $$ Mosquito make angle $${	an ^{ - 1}}\left( {{\sqrt {85} } \over 6}ight)$$ from y-axis.

Answer

$${	an ^{ - 1}}\left( {{\sqrt {85} } \over 6}ight)$$ from y-axis

Answer

$${	an ^{ - 1}}\left( {{5 \over 2}} ight)$$ from y-axis

Answer

$${	an ^{ - 1}}\left( {{2 \over 3}} ight)$$ from x-axis

Answer

$${	an ^{ - 1}}\left( {{5 \over 2}} ight)$$ from x-axis

Motion in 2D & Vectors

A mosquito is moving with a velocity $\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?

Choose the correct answer: