Question

A hot air balloon is released into the air. During its straight ascent, the angle of elevation was 15° and, 3 minutes later, the angle of elevation increased 20°. How fast is the balloon traveling, in km/h, if the angle measurements were taken 300m away from the launch site?

Answer 1

The speed of balloon is 0.16 m/s.

Explanation:

BC = 300 m

AD = x

AB = y

time, t = 3 min = 3 x 60 = 180 s

By the triangle, ADC,

`tan 15 = (AD)/(BC)\\\\0.27 * 300 = x \\\\x = 80.4 m`

By the triangle, BDC

`tan 20 = (BD)/(BC)\\\\0.36 * 300 = x + y \\\\x + y = 109.2 m`

So, y = 109.2 - 80.4 = 28.8 m

Speed of balloon = 28.8/180 = 0.16 m/s