Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at 3.9 m/s and 6.3 m/s. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) What is the speed (in m/s) of the boats relative to the river? 3.2 m/s (b) How fast is the river moving (in m/s) relative to the shore? 0.71 X m/s

A plane travels 4 km east and finds itself 5 km North and East of its starting point. Find the y component of the plane's motion and the angle the plane's displacement makes with the x-axis.  (Please explain in steps. I know the answer, but I need help understanding how to get there. Thank you.)

Boat A is stationary relative to the still water of a lake . Let the water surface be the xy plane . Boat B is moving at a constant speed of 3 m / s along the x - axis , relative to the water . According to an observer on A , a fish F has an acceleration of 7 m/s^ ^ 2a along the positive y axis . Which of the following vectors gives the acceleration of F as seen by an observer on B (inm / (s ^ 2)) ?

At noon, ship A is 70 km west of ship B. Ship A is sailing north at 28 km/h and ship B is sailing south at 28 km/h. How fast is the distance between the ships changing at 3 PM?

An airplane takes 5 hours to travel a distance of 4500 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind.

Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at 4.0 m/s and 5.0 m/s. (a) What is the speed of the boats relative to the river? (b) How fast is the river moving relative to the shore?

The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by the GPS system. In the LORAN system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference |PA| = |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). coastline 430 mi transmitting stations P B Suppose that station B is located 430 mi due east of station A on a coastline. A ship received the signal from B 1,200 microseconds (us) before it received the signal from A. (a) Assuming that radio signals travel at a speed of 980 ft/µs, find an equation of the hyperbola on which the ship lies. (Use x as the axis along the coastline, and center your coordinate system between A and B. Values should be in miles.) (b) If the ship is due north of B,…

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?