(III) Two cars approach a street corner at right angles to each other (Fig. 3–47). Car 1 travels at a speed relative to Earth vIE = 35 km/h, and car 2 at v2E = 55 km/h. What is the relative 2 velocity of car 1 as seen by car 2? What is the velocity of car 2 relative to car 1? 2E 1E FIGURE 3-47 Problem 51.

In the figure, you throw a ball toward a wall at speed 23.0 m/s and at angle θ0 = 36.0˚ above the horizontal. The wall is distance d = 21.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall?

- (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.

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. 3-53. What minimum pushoff speed is neces- sary to clear the rocks? How long are they in the air? 35 m |5.0 m| FIGURE 3-53 Problem 64.

(II) Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910 m in Yosemite National Park. Assume a jumper runs horizontally off the top of El Capitan with speed 4.0 m/s and enjoys a free fall until she is 150 m above the valley floor, at which time she opens her parachute (Fig. 3–37). (a) How long is the jumper in free fall? Ignore air resis- tance. (b) It is important to be as far away from the cliff as possible before opening the parachute. How far from the cliff is this jumper when she opens her chute? 4.0 m/s 910 m 150 m FIGURE 3-37 Problem 26.

2-27. Derive the equation for the range of a projectile fired on level ground, u* sin 20 R where R is the range, 0 is the angle of elevation, and u is the initial velocity. Show that the maximum range is achieved when 0 = 45°.

(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.

(I) A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

(II) A person in the passenger basket of a hot-air balloon throws a ball horizontally outward from the basket with speed 10.0 m/s (Fig. 3–44). What initial velocity (magni- tude and direction) does the ball have relative to a person standing on the ground (a) if the hot-air balloon is rising at 3.0 m/s relative to the ground during this throw, (b) if the hot-air balloon is descending at 3.0 m/s relative to the ground? 10.0 m/s FIGURE 3-44 Problem 43.