A jetliner can fly 6.00 hours on a full load of fuel. Without wind it flies at a speed of 2.40 X 102m/s. The planes to make a round-trip by heading due west for a certain distance,turning around, and then heading due east for the return trip.During the entire flight, however, the place encounters a 57.8 m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home ?

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dieseisB · Accepted Answer

The jetliner can fly for 6 hrs on a load of fuel, so the whole trip would have to take 6 hours. So that is 6 hrs×(60(60))sec⁡onds1 hr =21600 seconds it can fly and at 120 ms⋅21600 s=2592 km is how far the plane can travel in the round trip. let&#039;s see a diagram:  you can see that the wind counteracts the velocity of the plane on the departure flight so the velocity of the plane will be (240−57.8)=182.2m/s on the way back, the wind and plane velocity will add up sothe total velocity will be (240+57.8)=297.8m/s so we can say: so on the way back the plane travels (297.8−182.2)=115.6 m/sfaster than on the departure. the distance both ways must be the same so: distance there =182.2 ms⋅t1 distance back =297.8 ms⋅t2 for every if we take the ratio of these 2 : 297.8182.2 =1.6345 how many times faster the return time isthat the departure. t1=1.6345t2. the total time (t1+t2 must be 6 hrs or 21 600 seconds) so substitute in the above to get: (1.6345t2)+t2=21600 seconds. 2.6345t2=21600 s t2=8198.899 seconds. so t1 must be 21600−8198.899=13401.1 seconds. now we can plug this into our distane formula above: distance there =182.2 ms⋅13401.1 s=2441680 m=2.44⋅106 m is the distance that the plance can travel

xleb123 · Accepted Answer

Step 1:Let&#039;s denote the maximum distance traveled due west as d (in meters).When the plane flies due west, it will be flying against the wind, so its effective speed will be reduced. The plane&#039;s effective speed can be calculated as the difference between its actual speed and the wind speed:Veffective=Vplane−Vwind where Vplane is the plane&#039;s speed without wind (given as 2.40×102 m/s) and Vwind is the wind speed (given as 57.8 m/s).Therefore, the effective speed when flying due west is:Veffective=(2.40×102)−57.8 m/s.The total time spent flying due west is the distance traveled divided by the effective speed:twest=dVeffective.Similarly, the total time spent flying due east is the distance traveled divided by the sum of the plane&#039;s speed and the wind speed:teast=d(2.40×102)+57.8.Since the total flying time is 6 hours, the sum of the times spent flying west and east must be equal to 6:twest+teast=6.Substituting the expressions for twest and teast, we get:dVeffective+d(2.40×102)+57.8=6.Simplifying the equation and solving for d, we can find the maximum distance traveled due west:d=6×Veffective1+Veffective(2.40×102)+57.8.Step 2:Now we can substitute the given values for Veffective, solve the equation, and find the maximum distance traveled due west.d=6×(2.40×102−57.8)1+2.40×102−57.82.40×102+57.8Simplifying the expression further:d=6×(182.2)1+182.2240+57.8d=6×182.21+182.2297.8d=1093.21+0.6113d=1093.21.6113d≈678.40 metersTherefore, the maximum distance that the plane can travel due west and still be able to return home is approximately 678.40 meters.

fudzisako · Accepted Answer

When the plane is flying due west, the effective speed is the sum of the plane&#039;s speed and the speed of the wind blowing in the opposite direction. So, the effective speed while flying west is 2.40×102m/s−57.8m/s.The time taken to travel this distance can be calculated using the formula t=dv, where d is the distance and v is the velocity.Thus, the time taken to travel x meters due west is given by:twest=x2.40×102−57.8Since the total flight time is 6.00 hours, the time taken for the return trip is given by:teast=6.00−twestDuring the return trip, the effective speed while flying east is the sum of the plane&#039;s speed and the speed of the wind blowing in the same direction. So, the effective speed while flying east is 2.40×102m/s+57.8m/s.Using the same formula as before, the distance traveled during the return trip is:deast=teast×(2.40×102+57.8)Since the plane needs to return home, the distance traveled due west and due east must be the same. Therefore, we can set x equal to deast:x=teast×(2.40×102+57.8)Now, we can substitute the value of teast from the earlier equation:x=(6.00−twest)×(2.40×102+57.8)Substituting the value of twest from the first equation, we have:x=(6.00−x2.40×102−57.8)×(2.40×102+57.8)Now, we can solve this equation to find the value of x:x=(6.00−x2.40×102−57.8)×(2.40×102+57.8)Simplifying this equation will give us the maximum distance that the plane can travel due west and still be able to return home.

Jazz Frenia · Accepted Answer

Answer:546.6 metersExplanation:To find the maximum distance the plane can travel due west and still be able to return home, we need to consider the effect of the wind on the plane&#039;s speed.Let&#039;s denote the maximum distance the plane can travel due west as d (in meters).When the plane is flying due west, it will be flying against the wind, which will reduce its effective speed. The effective speed of the plane can be calculated by subtracting the wind speed from the plane&#039;s speed:Veffective=Vplane−VwindVeffective=2.40×102m/s−57.8m/sDuring the westward trip, the plane will take dVeffective hours to travel the distance d.Now, for the eastward trip, the plane will be flying with the wind, which will increase its effective speed. The effective speed for the eastward trip can be calculated by adding the wind speed to the plane&#039;s speed:Veffective=Vplane+VwindVeffective=2.40×102m/s+57.8m/sDuring the eastward trip, the plane will take dVeffective hours to travel the same distance d.Since the total flight time is given as 6.00 hours, the sum of the westward and eastward trip times must equal 6.00 hours:dVeffective+dVeffective=6.00Simplifying the equation:2·dVeffective=6.002dVeffective=6.00Solving for d:d=6.00·Veffective2Substituting the values of Veffective:d=6.00·(2.40×102m/s−57.8m/s)2d=6.00·182.2m/s2d=546.6mTherefore, the maximum distance the plane can travel due west and still be able to return home is 546.6 meters.

A jetliner can fly 6.00 hours on a full load of fuel. Without wind it flies at a speed of 2.40 X 102m/s. The planes to make a round-trip by heading du

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