Two friends are travelling downstream on a raft drifting along with the same speed as the river. At ? =0, Friend-1 jumps off the raft and start swimming downstream. At ? =30 ???, Friend-1 turns around and starts swimming upstream until he reaches the raft. By this time the raft has drifted 2 ?? downstream. Friend-1 swims at a constant speed relative to the river. a) Find the speed of the river. b) How does your answer to part a) depend on the Friend-1’s speed relative to the river? Hint: The speed of the river is independent of the Friend-1’s Speed.

Problems 74 and 75 are paired. 74. N A classroom clock has a small magnifying glass embedded near the end of the minute hand. The magnifying glass may be modeled as a particle. Class begins at 7:55 and ends at 8:50. The length of the minute hand is 0.300 m. a. Find the average velocity of the magnifying glass at the end of the minute hand using the coordinate system shown in Figure P3.74. Give your answer in component form. b. Find the magnitude and direction of the average velocity. c. Find the average speed and in the CHECK and THINK step, compare to the average velocity.

A police car traveling at 95.0 km/h is traveling west, chasing a motorist traveling at 80.0 km/h. (a) What is the velocity of the motorist relative to the police car? (b) What is the velocity of the police cat relative to the motorist? (c) If they are originally 250 m apart, in what time interval will the police car over take the motorist?

An airplane maintains a speed of 630 km/h relative to the air it is flying through as it makes a trip to a city 750 km away to the north. (a) What time interval is required for the trip if the plane flies through a head-wind blowing at 35.0 km/h toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 km/h to the east relative to the ground?

1) A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 h. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. What is his speed in still air, and how fast is the wind blowing? a. what is the speed (mph) in still air? b. wind speed (mph)?   2)A boat on a river travels downstream between two points, 60 mi apart, in 1 h. The return trip against the current takes 2 1/2 hours.  a. What is the boat's speed (in still water)? b. How fast does the current river flow?

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a headwind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 30 minutes. What is the plane's speed in still air, and how fast is the wind blowing?A. his plane speed equals mph.?   B. the wind speed equals mph.?

. Car A moves due East at 30 kph at the same instant car B is moving S 30° E, with a speed of 60 kph. The distance from A to B is 30 km. Find how fast is the distance between them separating after one hour. A. 36 kph B. 38 kph G. 40 kph D. 45 kph A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same point at 2:00 P.M. travels north at 45 kph. Find how (in kph) fast the two are separating at 4:00 P.M.? A. 49 B. 51 C. 53 D. 55 What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. m., if the error of the computed volume is not to exceed 0.03 cu. m? A. B. 0.002 0.003 0.0025 C. D. 0.001 75.A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at the rate of 0.03 ohm/sec, at what rate is the current "I" changing at the instant when the resistance is 6 ohms? Assume Ohm's law E = IR. A. -0.002 amp/sec B. 0.004 amp/sec C. -0.001 amp/sec D. 0.003 amp/sec

A rabbit runs across a parking lot on which a set of coordinate axis has been drawn. The coordinates of the rabbit’s position as a function of time t are given by:                            x = -0.3t2 + 5t + 28  and  y = 0.22t2 - 8t + 30 with t in seconds and x and y in meters. What is the velocity at t= 10 sec?      A. 0.6 i + 0.4 j   B. -0.2i +1.6j +30   C. -i - 3.6 j   D. 4i + 2j

Glenda and Harold are attempting to cross a river in a kayak. The river flows due east at 1.9 m/s. Glenda and Harold head the kayak due north and row at 2.4 m/s (relative to the water). The river is 38 m wide at this location. a. Determine the resultant velocity of the boat - both magnitude and direction.b. Determine the time for Glenda and Harold to cross the river.c. How far downstream will the boat be when Glenda and Harold reach the opposite shore?

Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to a field and lets them loose to exercise. Both dogs sprint away in different directions while Daniel stands still. From Daniel's point of view, Newton runs due north at 4.15 m/s, but from Pauli's point of view, Newton appears to be moving at 1.50 m/s due east. What is Pauli's velocity relative to Daniel, ?⃗PD? Give your answer in unit vector notation, where north is taken to be the positive ?-direction and east is the positive ?-direction. ?⃗PD=?ı̂+?ȷ̂ ?=??? m/s   ?=???? m/s   Next, express your answer as a magnitude and an angle measured counterclockwise from due east. magnitude=??? m/s   angle=??? ∘  counterclockwise from due east