Concept explainers
A fisherman sets out upstream on a river. His small boat, powered by an outboard motor, travels at a constant speed v in still water. The water (Urn’s at a lower constant speed vw. The fisherman has traveled upstream for 2.00 km when his ice chest falls out of the boat. He notices that the chest is missing only after he has gone upstream for another 15.0 min. At that point, he turns around and heads back downstream, all the time traveling at the same speed relative to the water. He catches up with the floating ice chest just as he returns to his starting point. How last is the river flowing? Solve this problem in two ways. (a) First, use the Earth as a reference frame. With respect to the Earth, the boat travels upstream at speed v − vw, and downstream at v + vw. (b) A second much simpler and more elegant solution is obtained by using the water as the reference frame. This approach has important applications in many more complicated problems; examples are calculating the motion of rockets and satellites and analyzing the scattering of subatomic particles from massive targets.
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Chapter 4 Solutions
Physics for Scientists and Engineers
- W S and X H 3 7. The captain of a small plane starts his journey by proceeding west. The speed of the plane with respect to still air is 170 km/h. A sudden south wind starts to blow at a constant speed of 87.5 km/h. What is the speed of the plane relative to the ground if no action is taken by the km/h E D C a R F V T C MacBook Air Ĝ 15 B Y 7 H N 8 Dil K M command opticarrow_forwardA boat leaves the dock at t = 0 and heads out into a lake. The wind gives the boat an initial velocity of 2.0m/si – 3.0m/sj. The boat accelerates at 1.5m/s'? + 1.2m/s'}. Find the position of the boat and its velocity att = 15 s. Assume the boat is at the origin at t = 0.arrow_forwardSITUATION 9. A small projectile is fired vertically downward into a fluid medium with an initial velocity of 60m/s. Due to the drag resistance of the fluid the projectile experiences a deceleration of a = -0.4v³m/s², where v is in m/s. Determine the projectile's velocity and position 4 s after it is fired.arrow_forward
- You are working as an expert witness for the defense of a container ship captain whose ship ran into a reef surrounding an island. The captain is being charged with intentionally running the ship into the reef. In discovery, the following information is correct: The ship was traveling at 2.5 m/s toward the reef when a mechanical failure caused the rudder to jam in the straight-ahead position. At that point in time, the ship was 900 m from the reef. The wind was blowing directly toward the reef and exerting a constant force of 9.00 x 103 N on the boat in a direction toward the reef. The mass of the ship and its cargo was 5.50 x 107kg. During the preparation for the trial, the captain claims that without control of the direction of travel, the only choice he had was to put the engines in reverse at maximum power, such that the total force exerted by the frictional drag force of the water on the propeller was 1.25 x 105 N in a direction away from the reef. From this information, construct…arrow_forwardYou need to get into your fourth-floor apartment, but you have forgotten your key to the main ground floor door of the building. You call up to your lazy roommate to come down and let you in, but he says he will throw the keys down to you instead. The window that he throws the keys out of is 13 meters above the ground, and he chucks them with a speed of 2m/s at an angle of 20 degrees above horizontal. The acceleration due to gravity near the surface of earth is 9.8 m/s?. How far back from the window do you need to stand to catch the keys?arrow_forwardOne side of the roof of a house slopes up at 37 deg. A roofer kicks a round, flat rock that has been thrown into the roof by a neighborhood child. The rock slides straight up the incline with an initial speed of 15 m/s. The coef. of friction between the rock and the roof is 0.40. The rock slides 10.0 m up the roof to its peak. It crosses the ridge and goes into free fall, following a parabolic trajectory above the far side of the roof, with negligible air resistance. Determine the maximum height the rock reaches above the point where it was kicked.arrow_forward
- A skier is at the top of a hill with height h. Starting from rest, the skier goes down to a flat area. On this flat area, there is a section of the slope with length D where the snow has melted (there is friction here). After passing the melted section, the skier goes up a smaller hill of height h2. At the top of this hill there is a drop off and the skier launches off of it with a horizontal speed. At what horizontal distance from the base of the jump does the skier land?arrow_forwardA catapult lunches a rock at a castle wall. The rock is lunched at a 45 degree angle with a speed of 22 m/s. the castle wall is 45 m away and is 20 m high. Does the rock make it over the wall?arrow_forwardYou are the captain of the John Paul Jones, Class-A Battleship on your way to kill the alien ship on the North side of Oahu, Hawaii. Your ship travels 10.36km [W650S] and then 5.60 km [S450W] to meet up with the alien ship. Determine your ship’s total displacement.arrow_forward
- In the Marvel comic series X-Men, Colossus would sometimes throw Wolverine toward an enemy in what was called a fastball special. Suppose Colossus throws Wolverine at an angle of e = 26.4° with respect to the ground (see figure below). Wolverine is d = 2.26 m above the ground when he is released, and he leaves Colossus's hands with a speed of v, = 16.0 m/s. (a) Using conservation of energy and the components of the initial velocity, find the maximum height attained by Wolverine during the flight. m (b) Using conservation of energy, what is Wolverine's speed the instant before he hits the ground? m/sarrow_forwardIn an attempt to escape his island, Gilligan builds a raftand sets to sea. The wind shifts a great deal during the day,and he is blown along the following straight lines: 2.50 km45.0º north of west; then 4.70 km 60.0º south of east;then 1.30 km 25.0º south of west; then 5.10 km straighteast; then 1.70 km 5.00º east of north; then 7.20 km55.0º south of west; and finally 2.80 km 10.0º north ofeast. What is his final position relative to the island?24. Suppose a pilot flies 40.0 km in a direction 60º north ofeast and then flies 30.0 km in a direction 15º north of east .Find her total distance R from thestarting point and the direction θ of the straight-line path tothe final position. Discuss qualitatively how this flight would bealtered by a wind from the north and how the effect of the wind would depend on both wind speed and the speed of theplane relative to the air massarrow_forwardA skier with a mass of 63.0 kg starts from rest and skis down an icy slope that has a length of 53.0 m at an angle of 32 degrees with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of 122m along the horizontal path. What is the speed of the skier at the bottom of the slope? What is the coefficient of kinetic friction between the skier and the horizontal surface?arrow_forward
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