Answer to Question #243012 in Mechanics | Relativity for Hud

Question

a bee flies to a flower 545 meters due north of its hive. the bee's speed in still air is 0.76 m/s, and there is a wind blowing toward the south at 0.24 m/s. How long will it take the bee to travel to the flower and back to the hive?

Answer 1

Explanations & Calculations

• If there were not that wind the bee would have flown at the speed of 0.76 m/s. With that wind hindering its motion, its speed is reduced by some amount.
• Since the directions are all in the same straight line, it is easy to find the final velocity.
• It will be

$\qquad\qquad \begin{aligned} \small \vec{V_{b,w}}&=\small\, \uparrow 0.76\,ms^{-1} \\ \small \vec{V_{w.E}} &=\small \, \downarrow 0.24\,ms^{-1}\\ \small V_{final}&=\small \vec{V_{b,E}}=V_{b,w}+V_{w,E}\\ &=\small \uparrow0.76+ \downarrow0.24\\ &=\small \uparrow0.76-\uparrow0.24\\ &=\small \uparrow 0.52\,ms^{-1} \end{aligned}$

• Then the time it may take to reach the flower,

$\qquad\qquad \begin{aligned} \small t&=\small \frac{S}{V}=\frac{545\,m}{0.52\,ms^{-1}}\\ &=\small 1048.08\,s\\ &\approx\small 17\,min \end{aligned}$

• Therefore, the total time for the trip will be $\small 2\times 17 \approx34\,min$