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Nady [450]
3 years ago
9

A plane leaves Seattle, flies 76.0 mi at 22.0 ∘ north of east, and then changes direction to 51.0 ∘ south of east. After flying

at 123 mi in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.
In what direction should the crew fly to go directly to the field? Use components to solve this problem

How far should the crew fly to go directly to the field? Use components to solve this problem.
Physics
1 answer:
mote1985 [20]3 years ago
5 0
This can be solve by using a triangle, because the path of the plane formed a triangle. first solve the angle form by the second direction
angle = 180 - 51 - 22 = 107 degrees
then using the cosine law
c^2 = a^2 + b^2 - 2ab cos C
c^2 = 76^2 + 123^2 - 2 ( 76) ( 123) cos ( 107)
c = 162.4 mi <span>the crew fly to go directly to the field
</span>
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A quarterback passes a football from height h = 2.1 m above the field, with initial velocity v0 = 13.5 m/s at an angle θ = 32° a
SOVA2 [1]

Answer:

a)    x = v₀² sin 2θ / g

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c)    x = 16.7 m

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This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity

        sin θ = v_{oy} / vo

        cos θ = v₀ₓ / vo

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a) In the x axis there is no acceleration so the velocity is constant

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          x = v₀ₓ t

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          v_{y} = v_{oy} - gt

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          t = v_{o} sin θ / g

         

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       x = v₀ cos θ (2 v_{o} sin θ / g)

       x = v₀² /g      2 cos θ sin θ

       x = v₀² sin 2θ / g

at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,

b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time

at the highest point the vertical speed is zero

          v_{y} = v_{oy} - gt

          v_{y} = 0

           t = v_{oy} / g

           t = v₀ sin θ / g

as the time to get on and off is the same the total time or flight time is

           t_total = 2 t

           t_total = 2 v₀ sin θ / g

c) we calculate

          x = 13.5 2 sin (2 32) / 9.8

          x = 16.7 m

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