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A hot-air balloon descends with a velocity of 55 km/h at an angle of 370 below the horizontal. What is the vertical velocity of the balloon?

User Gardenia
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Final answer:

The vertical velocity of the hot-air balloon is calculated using the sine function, where the clockwise angle is taken as negative because it's below the horizontal.

Step-by-step explanation:

The student is asking about the vertical velocity component of a hot-air balloon's descent. To find this vertical velocity, we must use trigonometry, specifically the sine function since the angle given is below the horizontal. First, convert the velocity from km/h to m/s by dividing by 3.6 (since 1 km/h equals approximately 0.27778 m/s). Now, calculate the vertical velocity (vvertical) using the formula vvertical = v * sin(θ), where v is the total velocity and θ is the angle of descent.

v = 55 km/h = 55 / 3.6 m/s

θ = 37° below the horizontal

vvertical = v * sin(θ) = (55 / 3.6) * sin(37°)

Perform the calculation to find the vertical velocity, keeping in mind that the answer will be negative because the direction is downwards.

User Nithinjith
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