A hot air balloon descends with an overall velocity of 4.2 m/s at an angle of 36.8⁰ below the horizontal. what is the horizontal velocity of the balloon?
To find the horizontal velocity of the balloon, we can use trigonometric functions.
The overall velocity of the balloon consists of both horizontal and vertical components. The vertical component is given as 4.2 m/s at an angle of 36.8 degrees below the horizontal.
To find the horizontal component, we need to use the cosine function because the cosine function relates the adjacent side (horizontal component) to the hypotenuse (overall velocity).
So we can use the equation:
cos(angle) = adjacent / hypotenuse
cos(36.8 degrees) = horizontal velocity / 4.2 m/s
Now we can solve for the horizontal velocity:
horizontal velocity = cos(36.8 degrees) × 4.2 m/s
Using a scientific calculator, we can find that cos(36.8 degrees) is approximately 0.801.
Therefore, the horizontal velocity of the hot air balloon is:
horizontal velocity = 0.801 × 4.2 m/s
horizontal velocity ≈ 3.36 m/s
So the horizontal velocity of the balloon is approximately 3.36 m/s.