You are flying a kite on windy day where the wind is blowing

You are flying a kite on windy day, where the wind is blowing horizontally. After 5 minutes of kite flying, the kite is at a height of 20ft from the ground, and the kite string forms a 34 degree angle with the ground, as shown below. The wind then takes the kite further away, but its height does not change, so that after 10 minutes the kite is now 50 feet from where you are standing. After 5 minutes, how far is the kite from where you are standing? That is, what is the distance shown by the dashed line? After 10 minutes, what angle does the kite string form with the ground? That is, what is theta? What is the change in the horizontal distance between you and the kite in the period from 5 minutes to 10 minutes?

Solution

a) The distance of kite from me = 20*csc34 = 35.8 ft

b) 20/50 = sin(theta)

Theta = 23.6 degree

c) After 5 min, distance = x1 = 20*cot34 = 29.65 ft

After 10 min, distance = x2 = 20*cot23.6 = 45.78 ft

Change in horizontal distance = x2 – x1 = 16.13 ft