A boat on a river is traveling from a pier to a point 500 m upstream (against the river's current). The current flows at 4 m/s. If the boat makes the trip in 250 s, what is the speed of the boat relative to the water?

(II) Raindrops make an angle θ with the vertical when viewed through a moving train window (Fig. 3–55). If the speed of the train is vₜ , what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?

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(II) (a) At what upstream angle must the swimmer in Problem 71 aim, if she is to arrive at a point directly across the stream? (b) How long will it take her?

(II) An airplane is heading due south at a speed of 688 km/h. If a wind begins blowing from the southwest at a speed of 85.0 km/h (average), calculate 

(a) the velocity (magnitude and direction) of the plane, relative to the ground, and . [Hint: First draw a diagram.]

(II) A motorboat whose speed in still water is 4.30 m/s must aim upstream at an angle of 23.5° (with respect to a line perpendicular to the shore) in order to travel directly across the stream. 

(b) What is the resultant speed of the boat with respect to the shore? (See Fig. 3–33.)