y B (B=26.5) 56.0° A (A = 44.0) 28.0° C(C= 31.0) x 15. (II) For the vectors shown in Fig. 3-41, determine (a) B-2A, (b) 2A - 3B + 2C.

(I). The motions of two objects, A and B, are defined by the following vectors: vector A = 6.0622i + 3.500j m/s vector B = 5.9500i - 10.3057j m/s unit vector of bullet = -j Object A and B left at the same time and at the same point. Object A aims to hit object B by firing a bullet in the direction stated above after 20 seconds. a). What should be the velocity of the bullet so that it will hit object B? b). What is the distance between object A and B the moment the bullet hits object B? c). What is the velocity vector of the bullet?

FIGURE 3-33 e Problem 7. west of north (Fig. 3–34). (a) Find the components of the velocity vector in the northerly and westerly direc- (835 km/h) tions. (b) How far north and how far west has the plane traveled after 1.75 h? 41.5 W FIGURE 3-34

63. The cliff divers of Acapulco push off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. 3-44. What minimum pushoff speed is necessary to clear the rocks? How long are they in the air? 35 m 5.0 m FIGURE 3-44 Problem 63.

(II) A rescue plane wants to drop supplies to isolated moun- tain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 250 km/h (69.4 m/s), how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. 3–38)? Vx0 "Dropped" (vyo=0) 235 m FIGURE 3-38 Problem 31.

(I) Huck Finn walks at a speed of 0.70 m/s across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The heavy raft is traveling down the Mississippi River at a speed of 1.50 m/s relative to the river bank (Fig. 3–42). What is Huck's velocity (speed and direction) relative to the river bank? 0.70 m/s River current FIGURE 3-42 Problem 39.

- (II) A child, who is 45 m from the bank of a river, is being carried helplessly downstream by the river's swift current of 1.0 m/s. As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line (Fig. 3–46) until she reaches the child at a point downstream. If the lifeguard can swim at a speed of 2.0 m/s relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child? 1.0 m/s 2.0 m/s - 45 m FIGURE 3-46 Problem 49.

(II) Figure 3–33 shows two vectors, A and B, whose magni- tudes are A = 6.8 units and B = 5.5 units. Determine Č if (a) Č = Ã + B, (b) Č = Ā – B, (c) Č = B – Ā. Give the magnitude and direction for each. - y В FIGURE 3–33 Problem 7.

As shown in Fig. 2-5, a projectile is fired horizontally with a speed of 30 m/s from the top of a cliff 80 m high. (a) How long will it take to strike the level ground at the base of the cliff? (b) How far from the foot of the cliff will it strike? (c) With what velocity will it strike? v₁" - 30 m/s 80 m X Fig. 2-5 40 m/s 30 m/s 8