Another airplane is flying in a jei stream that is blowing at 45.0 m/s in a dire

Question

Another airplane is flying in a jei stream that is blowing at 45.0 m/s in a direction 20 degree south of east (as in Exercise 3.58). Its direction of motion relative to the Earth is 45.0 degree south of west, while its direction of travel relative to the air is 5.00 degree south of west. What is the airplane's speed relative to the air mass? (b) What is the airplane's speed relative to the Earth? A sandal Is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the (mu k = 0). Calculate the deceleration of a snow boarder going up 5.0 degree, slope assuming the coefficient of friction for waxed wood on wet snow. The result of Exercise 5.9 may be use but be careful to consider the fact that the snow boarder is going uphill. Explicitly show how you follow the steps in Problem-Solving Strategies. Calculate the acceleration of a skier heading down

Explanation / Answer

(60) let va be the plane's velocity relative to the air mass and ve be the plane's velocity relative to the earth respectively.

north component, we have

(ve) sin (180 + 45)0 = (va) sin (180 + 5)0 + v0 sin (-20)0

(ve) sin 2250 = (va) sin 1850 + (45 m/s) sin (-20)0

ve = [(va) sin 1850 + (45 m/s) sin (-20)0] / sin 2250                                                  { eq.1 }

east component, we have

(ve) cos (180 + 45)0 = (va) cos (180 + 5)0 + v0 cos (-20)0

(ve) cos 2250 = (va) cos 1850 + (45 m/s) cos (-20)0                                                      { eq.2 }

inserting the value of ve in eq.2,

{[(va) sin 1850 + (45 m/s) sin (-20)0] / sin 2250} cos 2250 = (va) cos 1850 + (45 m/s) cos (-20)0

{[(va) sin1850 + (45 m/s) sin -200] cot 2250 = (va) cos 1850 + (45 m/s) cos -200

(va) [sin 1850 cot 2250 - cos 1850] = (45 m/s) cos -200 - (45 m/s) sin -200 cot 2250

va = (45 m/s) [cos (-20)0 - sin (-20)0 cot 2250] / (sin 1850 cot 2250 - cos 1850)

va = 63.4 m/s

Now, using eq.1 -

ve = [(va) sin 1850 + (45 m/s) sin (-20)0] / sin 2250   

ve = [(63.4 m/s) sin 1850 + (45 m/s) sin -200] / sin 2250

ve = 29.5 m/s

(a) The airplane's speed relative to the air mass is 63.4 m/s.

(b) The airplane's speed relative to the earth is 29.5 m/s.

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