the ball left the hands of the player Establish the Cartesian coordinate system given in figure. According to the problem, we have x,=0m, yo =2 m, x=8m, y=3 m a, =-g Using the general equations x=xo+vo y=y Then 8=voc0s60°1(1) Solving equation (1)and (2), we have the speed at which the ball left the hands of the player is 3. A pilot flies a plane at a speed of 700 km/h with respect to the surrounding air. a wind is blowing to the northeast at a speed of 100 km/h. In what direction must the plane be aimed so that the resulting direction of the plane is due north? What is the ground speed of the aircraft? Solution: Establish the Cartesian coordinate system given in figure North 45° From the problem, we have vnG=100c0s4521+100sm45°j -700cos 0i+700sin 6 →-70c0+700iO)=vmo3-100c0s451-100n45the ball left the hands of the player. Solution: Establish the Cartesian coordinate system given in figure. According to the problem, we have x0 = 0 m, y0 = 2 m, x = 8 m, y = 3 m ay = −g .Using the general equations ⎪ ⎩ ⎪ ⎨ ⎧ = + + = + 2 0 0 0 0 2 1 y y v t a t x x v t y y x Then ⎪ ⎩ ⎪ ⎨ ⎧ = + ° − = ° (2) 2 1 3 2 sin 60 8 cos60 (1) 2 0 0 v t gt v t Solving equation (1) and (2), we have the speed at which the ball left the hands of the player is v0=9.88 m/s 3. A pilot flies a plane at a speed of 700 km/h with respect to the surrounding air. A wind is blowing to the northeast at a speed of 100 km/h. In what direction must the plane be aimed so that the resulting direction of the plane is due north? What is the ground speed of the aircraft? Solution: Establish the Cartesian coordinate system given in figure. According to PW PG WG v v v r r r = − From the problem, we have ⎪ ⎩ ⎪ ⎨ ⎧ = − + = = ° + ° v i j v v j v i j PW PG PG WG ˆ 700cos ˆ 700sin ˆ 45 ˆ 100cos45 ˆ 100sin θ θ r r r i j v j i j PG 45 ˆ 700cos ˆ 700sin ˆ ˆ 100cos45 ˆ 100sin o o ⇒ − θ + θ = − − y x 0 45° PG v v v PW v WG v v θ North East