Only practice problem 3.11. The second photo has background info to help solve the problem. relative to theframes ofgorean(3.14)he trainthatprs.veleS-.a tanREFLECT The plane's velocity with respect to the air is straight north,but the air's motion relative to earth gives the plane's velocity with re-spect to earth a component toward the east.EXAMPLE 3.11 Compensating for a crosswindThe lift and drag forces on an aircraft are functions of its velocity relative to the air, not to the ground. Conse-quently, pilots must compensate for the effects of wind. In this example we will determine in what directionthe pilot in Example 3.10 should head in order for the plane to travel due north. Then we will determine theplane's velocity relative to the earth. (We will assume that the wind velocity and the magnitude of the airspeedare the same as in Example 3.10.)SOLUTIONSET UP Now the information given isWe find thatB = sinH)+(100 km/h)2= 260 km/h,= 23° E of N.100 km/h240 km/hFigure 3.28 shows the appropriate vector diagram. Be sure you under-stand why this is not the same diagram as the one in Figure 3.27.1.SOLVE We want to find üp/E; its magnitude is unknown, but we knowthat its direction is due north. Note that both this and the preceding ex-ample require us to determine two unknown quantities. In Example 3.10,these were the magnitude and direction of UP/E; in this example, theunknowns are the direction of P/A and the magnitude of P/E-The three relative velocities must still satisfy the vector equationÜP/E = UP/A + UA/E-OP/A = 240 km/h direction unknown,VA/E = 100 km/h due east.100 km/h240 km/h= 25°,Practice Problem: If the plane maintains its airspeed of 240 km/h, butthe wind decreases, what is the wind speed if the plane's velocity withrespect to earth is 15° east of north? Answer: 64 km/h.UP/E = V(240 km/h)2 - (100 km/h)² = 218 km/h.The pilot should head 25° west of north; her ground speed will thenbe 218 km/h.► FIGURE 3.28 The pilot must pointthe plane in the direction of the vectorÜP/A in order to travel due north rela-tive to the earth.Video Tutor SolutionVA/E = 100 km/h,eastUP/A =240 km/h,at angle BWEUP/E,northREFLECT When a plane flies in a crosswind that is at right angles to theplane's velocity relative to the ground, its speed relative to the ground isalways slower than the airspeed; the trip takes longer than in calm air.Practice Problem: If the pilot was forced to reduce the plane's speedto 150 km/h, how much would she need to increase the angle at whichthe plane is pointing (relative to north) in order for the plane to continueto travel due north? Answer: 8.7°. Page 76- Practice Problem 3.6If the kicker gives the ball the same initial speed and anglebut the ball is kicked from a point 25m from the goalpost,what is the height of the ball above the crossbar as itcrosses over the goalpost? Answer: 1.2m.Page 77- Practice problem 3.7Suppose the pear is released from a height of 6.00m abovethe archer's arrow, the arrow is shot at a speed of 30.0m/s,and the distance between the archer and the base of thetower is 15.0m. Find the time at which the arrow hits thepear, the distance the pear has fallen, and the height of thearrow above its release point. Answers: 0.54s, 1.4m, 4.6m.Page 80-Practice Problem 3.8A more reasonable maximum acceleration for varyingpavement conditions is 5.0m/s². Under these conditions,what is the maximum speed at which a car can negotiate aflat curve with radius 230m? Answer: 34m/s=76mi/h.Page 81- Practice Problem 3.9If the ride increases in speed so that T = 2.0S, what is a rad?(this question can be answered by using proportionalreasoning, without much arithmetic.) Answer: 49 m/s².Page 83 - Practice Problem 3.10If the plane its airspeed of 240km/h, but the winddecreases, what is the wind speed if the plane's velocitywith respect to earth is 15° east of north? Answer: 64 km/h.Page 84 - Practice Problem 3.11If the pilot was forced to reduce the plane's speed to150km/h, how much would she need to increase the angleat which the plane is pointing (relative to north) in order forthe plane to continue to travel due north? Answer: 8.7°

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If the pilot was forced to reduce the plane's speed to 150km/h, how much would she need to increase the angle at which the plane is pointing (relative to north) in order for the plane to continue to travel due north? Answer: 8.7°