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3 years ago

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An airplane pilot sets a compass course due west and maintains an airspeed of 210 km/h. After flying for a time of 0.490 h, she

finds herself over a town a distance 121 km west and a distance 20 km south of her starting point.Find the magnitude of the wind velocity.

2 answers:

tankabanditka [31]3 years ago

5 0

Answer:

$V_{A/E}=55.23km/h\\or\\V_{A/E}=15.342m/s$

Explanation:

The velocity of plane relative to earth is given by:

$V_{P/E}=\frac{d}{t}\\V_{P/E}=\frac{[-121i-20j]km}{0.490h} \\V_{P/E}=[-247i-41j]km/h$

As the from given data.The velocity of plane relative to air is:

$V_{P/A}=[-210i]km/h$

According to relative motion of velocity of the air relative to earth given by:

$V_{A/E}=V_{P/E}-V_{P/A} \\V_{A/E}=[(-247i-41j)km/h]-(-210i)km/h\\V_{A/E}=[-37i-41j]km/h\\$

The magnitude is given as:

$V_{A/E}=\sqrt{(37)^{2}+(41)^{2} }\\ V_{A/E}=55.23km/h\\or\\V_{A/E}=15.342m/s$

Andrei [34K]3 years ago

5 0

Answer:

55km/h , 47.87° south west or 227.87°

Explanation:

If there is no wind then the plane would be at a distance

d=(210 km/h)(0.49h) = 102.9 km west of the starting point.

if the wind is blown then then the plane is 121 km - 102.9 km = 18.1 km west and 20 km south in the time 0.49 h.

Velocity of the plane in west direction=(18.1 km) / 0.49 h = 36.9 km/h

velocity of the plane in south direction=(20 km) / 0.49 h = 40.8 km/h

Now the wind velocity is

$\sqrt{(36.9^2 + 40.8^2}$

= 55.01 km/h

The direction is

θ =tan⁻¹ (40.8 / 36.9)

θ = 47.87° south west or 227.87°

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A boat leaves the dock at t = 0.00 s and, starting from rest, maintains a constant acceleration of (0.461 m/s2)i relative to the

liberstina [14]

Answer:

At t=4.82 s, the boat is moving at 3.464 m/s.

At t=4.82 s, the boat is 13.112 m from the dock.

Explanation:

The speed of the boat in j'th direction remains constant for all times (vj=2.16 m/s), however, the speed in i'th direction is changing due to the constant acceleration (0.461 m/s^2)i.

In order to find the velocity of the boat a t=4.82 s, first we need to compute the velocity of the boat relative to the water in the i direction (vi_b) at t=4.82 s:

vi_b = a*t = (0.461 m/s^2)*(4.82 s) = 2.222 m/s

Now, we add this velocity to the velocity of the water in the i direction:

vi = vi_b + vi_w = 2.222 m/s + 0.486 m/s = 2.708 m/s

Therefore, the speed of the boat at t = 4.82 s is: v = (vi, vj) = (2.708, 2.16) m/s. Finally, to find its speed, we just calculate the magnitude of v and obtain that the speed is: 3.464 m/s.

For the second question, first we will find the distance that the boat moved in the i'th direction and then in the j'th direction.

The speed in the i'th direction, for all times, is given by:

(0.485 + 0.461*t) and in order to find the distance advanced in the i'th direction (di) during 4.82 s, we need to integrate this velocity:

di = 0.485*t + (0.461*t^2)/2 (evaluated from t=0 to t =4.82) = 0.485*(4.82) + (0.461*(4.82)^2)/2 = 2.337 + 5.634 = 7.971 m

The speed in j'th direction, for all times, is given by:

2.16 and in order to find the distance advanced in the j'th direction (dj) during 4.82 s, we need to integrate this velocity:

dj = 2.16*t (evaluated from t=0 to t =4.82) = (2.16)*(4.82) = 10.411 m

Using Pythagoras' Theorem, we find that the the boat is at 13.112 m from the dock at t = 4.82 s.

4 0

3 years ago

A 6.72 particle moves through a region of space where an electric field of magnitude 1270 N/C points in the positive direction,

Romashka [77]

Answer:

$v_{y} = -104 m/s$

Explanation:

Using:

Force = electric field * charge

$F=e*q$

Force = magnitude of charge * velocity * magnetic field * sin tither

$F_{x2}= |q|*v*B*sin \alpha$

Force on particle due to electric field:

$F_{x1}= E*q = (1270N/C)*(-6.72*10^{-6} ) = -8.53*10^{-3}$

Force on particle due to magnetic field:

$F_{x2}= |q|*v*B*sin \alpha = (6.72*10^{-6} )*(1.15)*(sin90)*v = (7.728*10^{-6})*(v)$

$F_{x2}$ is in the positive x direction as $F_{x1}$ is in the negative x direction while net force is in the positive x direction.

Magnetic field is in the positive Z direction, net force is in the positive x direction.

According to right hand rule, Force acting on particle is perpendicular to the direction of magnetic field and velocity of particle. This would mean the force is along the y-axis. As this is a negatively charged particle, the direction of the velocity of the particle is reversed. Therefore velocity of particle, v, has to be in the negative y direction.

Now,

$F_{xnet}- F_{x1 } = F_{x2 }$

$(6.13*10^{-3}) - (8.53*10^{-3} ) = (7.728*10^{-6})*(v)$

$v = (F_{xnet} - F_{x1}) / (F_{x2} )$

$=((6.13*10^{-3} ) - (8.53*10^{-3})) / (7.728*10^{-6})$

$= (- 104.25) m/s$

$v_{y} = -104 m/s$

8 0

3 years ago

Study the velocity vs. time graph shown.

laiz [17]

For velocity vs Time graphs, the displacement of the object from 2 seconds to 6 seconds is 30 m.

<h3>What is displacement?</h3>

The displacement is the shortest distance travelled by the particle. It is the vector quantity which re[presents both the magnitude and direction.

In velocity time graphs, the displacement is the area under the curve of the graph on the x axis.

'

A line starts at (0, 2) and ends at (6, 8) in v-t graph

Displacement is equal to the area of a triangle and a rectangle formed under the line.

Area = 1/2 base x height + length x breadth

Area = 1/2 x 6x 6 + 6x2

Area = 18 +12

Area = 30 m

Thus, the displacement is 30 m.

Learn more about displacement.

brainly.com/question/11934397

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6 0

2 years ago

A 58.5 kg sprinter starts a race with an acceleration of 4.40 m/s2. What is the net external force on him?

mote1985 [20]

Answer:

External force on him = 257.40 N

Equation is; F = ma (where 'f' is force, 'm' is mass and 'a' is acceleration)

Explanation:

The mass of the sprinter is 58.5 kg

His acceleration is 4.40 m/s²

According to Newton's second law of motion; F = ma

External force on the sprinter = 58.5 kg × 4.40 m/s² = 257.40 N

4 0

3 years ago

A traffic light is weighing 200N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper

Levart [38]

Answer:

T₁ = 93.6 N , T₂ = 155.6 N , T₃ = 200 N

Explanation:

This is a balance exercise where we must apply the expressions for translational balance in the two axes

∑ F = 0

Suppose that cable t1 goes to the left and the angles are 41º with respect to the horizontal and cable t2 goes to the right with angles of 63º

decompose the tension of the two upper cables

cos 41 = T₁ₓ / T1

sin 41 = T₁y / T1

T₁ₓ = T₁ cos 41

T₁y= T₁ sin 41

for cable gold

cos 63 = T₂ / T₂

sin 63 = $T_{2y}$ / T₂

We apply the two-point equilibrium equation: The junction point of the three cables and the point where the traffic light joins the vertical cable.

Let's start by analyzing the point where the traffic light meets the vertical cable

T₃ - W = 0

T₃ = W

T₃ = 200 N

now let's write the equations for the single point of the three wires

X axis

- T₁ₓ + T₂ₓ = 0

T₁ₓ = T₂ₓ

T1 cos 41 = T2 cos 63

T1 = T2 cos 63 / cos 41 (1)

y Axis

$T_{1y}$ + T_{2y} - T3 = 0

T₁ sin 41 + T₂ sin 63 = T₃ (2)

to solve the system we substitute equation 1 in 2

T₂ cos 63 / cos 41 sin 41 + T₂ sin 63 = W

T₂ (cos 63 tan 41 + sin 63) = W

T₂ = W / (cos 63 tan 41 + sin 63)

We calculate

T₂ = 200 / (cos 63 tan 41 + sin 63)

T₂ = 200 / 1,2856

T₂ = 155.6 N

we substitute in 1

T₁ = T₂ cos 63 / cos 41

T₁ = 155.6 cos63 / cos 41

T₁ = 93.6 N

therefore the tension in each cable is

T₁ = 93.6 N

T₂ = 155.6 N

T₃ = 200 N

6 0

2 years ago