Question 24

The angle of elevation of a hot-air balloon climbing vertically changes from 30° at 10:00 AM to 60° at 10:02
AM as observed from a point 300 m away from the take-off point. What is the upward speed of the balloon?

Solution

H1 = 300 $$\times$$ tan 30

H2 = 300 $$\times$$ tan 60

Now,

H2 - H1 = 300 $$\times$$ (tan60 - tan30) = 300 $$\times$$ 1.155 =346.5

Time duration = 10:02 - 10:00 = 2 min = 120 sec.

Speed = height/time = 346.5/120 = 2.9 m/s

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The angle of elevation of a hot-air balloon climbing vertically changes from 30° at 10:00 AM to 60° at 10:02AM as observed from a point 300 m away from the take-off point. What is the upward speed of the balloon?