A cannon ball is fired from a cannon located on top of a 30.0 meter tall wall into the distance. The initial velocity of the cannonball coming out of the cannon is vo. The initial angle of launch of the cannon ball is 0. We want to determine how far from the base of the wall the cannonball will strike the ground (in the horizontal direction) if we are given the initial speed vo and angle 0. (A) Sketch a graph showing position of the cannonball during its flight (y versus x) showing and labeling the initial velocity vector. Identify and write knowns and unknowns (B) Without using numerical values, determine which physics equations of motion will help solve this problem. Simplify as useful for this particular case. (C) If the initial cannonball speed is 75.0 m/s and its initial angle is 0=32.0 degrees, how far horizontally from the base of the wall does the cannonball land?

A golfer tees off from a location precisely at i = 35.0 north latitude. He hits the ball due south, with range 285 m. The balls initial velocity is at 48.0 above the horizontal. Suppose air resistance is negligible for the golf ball. (a) For how long is the ball in flight? The cup is due south of the golfers location, and the golfer would have a hole-in-one if the Earth were not rotating. The Earths rotation makes the tee move in a circle of radius RE cos i = (6.37 106 m) cos 35.0 as shown in Figure P6.47. The tee completes one revolution each day. (b) Find the eastward speed of the tee relative to the stars. The hole is also moving cast, but it is 285 m farther south and thus at a slightly lower latitude f. Because the hole moves in a slightly larger circle, its speed must he greater than that of the tee. (c) By how much does the holes speed exceed that of the tee? During the time interval the ball is in flight, it moves upward and downward as well as southward with the projectile motion you studied in Chapter 4, but it also moves eastward with the speed you found in part (b). The hole moves to the east at a faster speed, however, pulling ahead of the ball with the relative speed you found in part (c). (d) How far to the west of the hole does the ball land? Figure P6.47

An airplane leaves city A and flies a distance d1 due north, landing at city B. The next day, the airplane leaves city B and flies a distance d2 in a direction making an angle to the east of due north, landing at city C. Determine the distance between city A and city C. Express your answer in terms of d1, d2, and .

Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r. u. and L respectively. Consider the quantity (-3 2t ). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?