A weather balloon rises upward at a rate of 6.4 m/s, but a wind blows it east at 4.8m/s. What is the resulting velocity? How long will it take to drift across a lake that is 12.0 km wide?
The weather balloon rises up at 6.4 m/s and the wind blows east at 4.8 m/s.
The resulting velocity of the balloon has a magnitude `sqrt(6.4^2 + 4.8^2) = 8`m/s . The direction of the resulting velocity makes an angle of `tan^-1(4.8/6.4)` to the vertical towards the east. This is approximately 36.86 degrees to the vertical towards the east.
The time taken by the balloon to drift across the river is dependent only on its horizontal velocity of 4.8 m/s. The time taken is 12000/4.8 = 25000 s.
The resulting velocity of the balloon is 8 m/s in a direction making an angle of 36.86 degrees towards the East with the vertical. It takes 25000 s to cross the lake.