A bird is resting on a phone wire between two poles that are 30 m apart. The bird is exactly midway between the two poles. Because of the weight of the bird, the wire sags by 50 cm. The tension in the wire is 70 N
To find the height at which the wire is sagging, we can use the Pythagorean theorem. Let's call the height of the sagging wire h.
According to the given information, the distance between the bird and each pole is 15 m (half the distance between the poles), and the wire sags by 50 cm (0.5 m).
Using the Pythagorean theorem, we have: (15)^2 = h^2 + (0.5)^2
Simplifying the equation: 225 = h^2 + 0.25
Rearranging the equation: h^2 = 225 - 0.25
h^2 = 224.75
Taking the square root of both sides: h = √224.75
Calculating the value: h ≈ 14.99 m
Therefore, the wire sags by approximately 14.99 m.
To find the horizontal distance between the poles, we can consider the sag in the wire as a right triangle. The distance between the midpoint of the wire (where the bird is) and one of the poles is equal to half the distance between the poles minus the sag in the wire.
Let's break down the problem and calculate the distance:
1. Half the distance between the two poles: 30 m / 2 = 15 m.
2. Subtracting the sag in the wire: 15 m - 0.5 m = 14.5 m.
Therefore, the horizontal distance between the midpoint of the wire (where the bird is) and one of the poles is 14.5 meters.
So what is the question? All you haven't been given is the weight of the bird.
Figure the angle at the center (vertical to wire) tanTheta=15/.5
Now, if tension is 70, and each side supports half the weight of the bird
then cosTheta=weight/2 / tension
and you solve for weight.