A mosquito is moving with a velocity v = 0.5t² i + 3t j + 9 k m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?
A mosquito is moving with a velocity v = 0.5t² i + 3t j + 9 k m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?
Option 1 -
tan⁻¹(2/3) from x-axis
Option 2 -
tan⁻¹(5/2) from y-axis
Option 3 -
tan⁻¹(5/2) from x-axis
Option 4 -
tan⁻¹(2/3) from y-axis
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:v = 0.5t² i + 3t j + 9 k m/s ⇒ a = dv/dt = (ti + 3j) m/s²
At t=2sec, v = 2i + 6j + 9k m/s and a = (2i + 3j) m/s²
The direction of acceleration of mosquito after 2s is given by the angle θ with the y-axis, where tanθ = a? /a? = 2/3.
So, the direction is tan? ¹ (2/3) from the y-axis.
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