Bird flies 80m east, then 60m south, then straight up

In to sky for 30m.
A)at this point how far is bird from his nest?

You should have a 3D diagram.

let the distance on the ground be x
x^2 = 80^2 + 60^2

let the distance from start to finish be y
y^2 = x^2 + 30^2
= 80^2 + 60^2 + 30^2
10900
y = √10900 = 104.4 m

or, using vectors
distance vector
= (0,80,0) + (60,0,0) + (0,0,30)
= )60,80,30)
magnitude = √(80^2 + 60^2 + 30^2)
= as before

To determine the distance of the bird from its nest, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this scenario, we can consider the bird's nest as the starting point (origin) of a coordinate plane. The bird flies 80m east, which means it moves 80 units to the right along the x-axis. Then, it goes 60m south, which translates to moving 60 units downward along the y-axis. Finally, it flies straight up into the sky for 30m, which doesn't affect the x and y coordinates.

Using the Pythagorean theorem, we can calculate the distance from the bird to its nest. Let's denote the distance from the nest as 'd.'

Using the formula:

d^2 = (80)^2 + (-60)^2 + (30)^2

d^2 = 6400 + 3600 + 900

d^2 = 10900

Taking the square root of both sides, we find:

d ≈ 104.4

Therefore, at this point, the bird is approximately 104.4 meters away from its nest.