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nekit [7.7K]
3 years ago
13

You're reading an article about forest fires in california and it features a photograph of firefighters battling a fire on a hil

lside next to a freeway. the firefighters are at the bottom of the hill using a firehose to control a fire that's in the middle of the hill. you're curious how fast the water is exiting the nozzle. analyzing the photograph in photoshop, you determine that the firehose nozzle is being held 2.1 m above the ground and is angled 43 ∘ above the horizontal. furthermore, the water from the hose lands on the hill 30 m from the feet of the firefighters. the article mentions that the grade of the hill is 37%, which corresponds to a slope of 20∘ above the horizontal. what is the speed the water when it exits the hose?

Physics
1 answer:
Lelechka [254]3 years ago
7 0
I will say it is about 20 m/s

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1. Two forces act on a box as follows: F1 = 100 N at 01 = 170° and F2 = 75 N
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Answer:

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Force F1

          sin 170 = F_{1y} / F₁

          cos 170 = F₁ₓ / F₁

          F_{1y} = F₁ sin 170

          F₁ₓ = F₁ cos 170

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          sin 30 = F_{2y} / F₂

          cos 30 = F₂ₓ / F₂

          F_{2y} = F₂ sin 30

          F₂ₓ = F₂ cos 30

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the resultant force is

X axis

          Fₓ = F₁ₓ + F₂ₓ

          Fₓ = -98.48 +64.95

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Y axis

         F_y = F_{1y} + F_{2y}

         F_y = 17.36 + 37.5

         F_y = 54.86 N

a) the magnitude of the resultant vector

let's use Pythagoras' theorem

         F = Ra Fx ^ 2 + Fy²

         F = Ra 33.53² + 54.86²

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b) the direction of the resultant

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        tan θ’= F_y / Fₓ

        θ'= tan^{-1}  \frac{F_y}{F_x}

        θ'= tan⁻¹ (54.86 / (33.53)

        θ’= 58.6º

this angle is in the second quadrant

The angle measured from the positive side of the x-axis is

        θ = 180 -θ'

        θ = 180- 58.6

        θ = 121.4º

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