A kite is hovering over the ground at the end of a straight 47-m line. The tension in the line has a magnitude of 14 N. Wind blowing on the kite exerts a force of 17 N, directed 55° above the horizontal. Note that the line attached to the kite is not oriented at an angle of 55° above the horizontal. Find the height of the kite, relative to the person holding the line.

Question

A kite is hovering over the ground at the end of a straight 47-m line. The tension in the line has a magnitude of 14 N. Wind blowing on the kite exerts a force of 17 N, directed 55° above the horizontal. Note that the line attached to the kite is not oriented at an angle of 55° above the horizontal. Find the height of the kite, relative to the person holding the line.

Answer 1

To find the height of the kite, we can break down the forces acting on it and use trigonometry to calculate the height.

First, let's visualize the situation. We have a kite hovering over the ground, attached to a line that is not oriented at an angle of 55°.

The tension in the line has a magnitude of 14 N, acting vertically upwards (opposite to the force of gravity). The wind blowing on the kite exerts a force of 17 N, directed 55° above the horizontal.

Now, let's resolve these forces into their vertical and horizontal components:

1. Tension Force: The tension force in the line can be broken down into its vertical (Tv) and horizontal (Th) components. Since the kite is hovering, the vertical component of tension force (Tv) must balance the force of gravity acting on the kite. Therefore, Tv = mg, where m is the mass of the kite (which we assume to be negligible) and g is the acceleration due to gravity (approximately 9.8 m/s²).

2. Wind Force: The wind force can also be broken down into its vertical (Wv) and horizontal (Wh) components. Since the wind force is directed 55° above the horizontal, we can use trigonometry to find its vertical component. Wv = W * sin(55°) = 17 N * sin(55°).

Now, let's calculate the vertical force acting on the kite:

Total Vertical Force (Fv) = Tv + Wv = mg + W * sin(55°)

Since we know the tension in the line is equal to its vertical component (Tv) and the length of the line (47 m), we can find the vertical force acting on the kite:

Tv = Fv = 14 N (given)

Now, let's calculate the height of the kite:

Height (h) = Fv / mg

Substituting the values we know:

h = 14 N / (m * 9.8 m/s²)

Since the mass of the kite (m) is negligible, we can assume it equals zero. Therefore, the height of the kite relative to the person holding the line is:

h = 14 N / (0 * 9.8 m/s²)
h = 0

Therefore, the height of the kite relative to the person holding the line is zero.