(13%) Problem 3: While watching the clouds pass by, you notice a European swallow flying horizontally at a height of h = 22.65 m. When the swallow is directly overhead, it drops an m = 11.7 kg coconut. Refer to the diagram. From your ornithological studies, you know that the air- speed of this particular species of swallow, while carrying such a load, is vo=7.88 m/s. Neglect air resistance. Assume that your head is at the origin of the coordinate system. 20 ▲ 20% Part (a) Calculate the magnitude, in kilogram squared meters per second, of the angular momentum of the coconut, as observed by you, at the moment it is released directly overhead. =▲ 20% Part (b) Let be the time-dependent position vector of the coconut with time measured from the instant it was released by the swallow. Enter an expression for its horizontal component as a function of time. 20% Part (c) Enter an expression, in unit vector notation, for the time-dependent velocity vector, (t), of the coconut. 20% Part (d) Calculate the magnitude, in kilogram squared meters per second, of the angular momentum of the coconut as observed by you at t = 1.0 s. L=2544 kg-m²/s ✓Correct! 20% Part (e) Calculate the magnitude, in kilogram squared meters per second, of the coconut as observed by you immediately before it hits the ground. L= kg - m²/s sin cos tan π cotan asin() acos() E ( ) 7 8 9 M4 5 6 HOME atan acotan() sinh 1 2 3 cosh tanh cotanh + - 0 END Degrees Radians NO BACKSPACE DEL CLEAR

You are lying in your bedroom, resting after doing your physics homework. As you stare at your ceiling, you come up with the idea for a new game. You grab a dart with a sticky nose and a mass of 19.0 g. You also grab a spring that has been lying on your desk from some previous project. You paint a target pattern on your ceiling. Your new game is to place the spring vertically on the floor, place the sticky-nose dart facing upward on the spring, and push the spring downward until the coils all press together, as on the right in Figure P7.26. You will then release the spring, firing the dart up toward the target on your ceiling, where its sticky nose will make it hang from the ceiling. The spring has an uncompressed end-to-end length of 5.00 cm, as shown on the left in Figure P7.26, and can be compressed to an end-to-end length of 1.00 cm when the coils are all pressed together. Before trying the game, you hold the upper end of the spring in one hand and hang a bundle of ten identical darts from the lower end of the spring. The spring extends by 1.00 cm due to the weight of the darts. You are so excited about the new game that, before doing a test of the game, you run out to gather your friends to show them. When your friends are in your room watching and you show them the first firing of your new game, why are you embarrassed?

Two calipers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5 km, and that along Path 2 is 82 km. What is the final displacement of each camper?

A bottle rocket is shot straight up in the air with a speed 30 m/s. if the air resistance is ignores, the bottle would go up to a height of approximately 46 m. however the rocket goes up to only 35 m before returning to the ground. What happened? Explain, giving only a qualitative response.

If the speed of a particle is doubled, what happens to its kinetic energy? (a) It becomes four times larger. (b) It becomes two times larger. (c) It becomes 2 times larger. (d) It is unchanged. (e) It becomes half as large.

Towns A and B in Figure P4.64 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2?

A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 2.35 m high, and from there it will fall into a pool (Fig. P4.22). (a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, which is one-twelfth actual size. How fast should the water flow in the channel in the model?

A suspicious physics student watches a stunt performed at an ice show. In the stunt, a performer shoots an arrow into a bale of hay (Fig. P11.24). Another performer rides on the bale of hay like a cowboy. After the arrow enters the bale, the balearrow system slides roughly 5 m along the ice. Estimate the initial speed of the arrow. Is there a trick to this stunt? FIGURE P11.24

A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 0 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the hall have maximum speed? (c) What is this maximum speed?

Unreasonable Results A mountain stream is 10.0 m wide and averages 2.00 m in depth. During the spring runoff, the flow in the stream reaches 100,000 m3/s. (a) What is the average velocity of the stream under these conditions? (b) What is unreasonable about this velocity? (c) What is unreasonable or inconsistent about the premises?