A runner is jogging in a straight line at a

Physics

1 answer:

soldi70 [24.7K]3 years ago

4 0

Answer:

13 km

Explanation:

The bird flies from the runner, to the finish line, and back to the runner. We can write two equations for the distance it travels:

d = 7.8 km + 7.8 km − 4.9 km/hr × t

d = 24.5 km/hr × t

Solve for t in the second equation and substitute into the first:

t = d / 24.5

d = 7.8 + 7.8 − 4.9 (d / 24.5)

d = 15.6 − 0.2 d

1.2 d = 15.6

d = 13

The bird flies a cumulative distance of 13 km.

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Blizzard [7]

We can approach this in another way.
We know that sin(∅) = height / hypotenuse.

Thus, for x, height is 1 and hypotenuse is 3. Using Pythagoras theorem,
3² = 1² + b²
b = √8
cos(x) = b/hypotenuse
cos(x) = √8 / 3

Now, lets consider y:
sec(y) = 1 / cos(y) = 1 / base / hypotenuse = hypotenuse / base
The hypotenuse is 25 and the base is 24. We again apply Pythagoras theorem to find the third side, which works out to be:
height = 7
sin(y) = height / hypotenuse
sin(y) = 7/25

Now, sin(x + y) =
sin(x)cos(y) + sin(y)cos(x)
= (1/3)(24/25) + (√8 / 3)(7/25)
= 8/25 + 7√8/75
= (24 + 14√2) / 75

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