Back(II) A swimmer is capable of swimming 0.60 m/s in still water. (a) If she aims her body directly across a 55-m-wide river whose current is 0.50 m/s, how far downstream (from a point opposite her starting point) will she land? (b) How long will it take her to reach the other side?
A child, who is 45 m from the bank of a river, is being carried helplessly downstream by the river's swift current of 1.0 m/s . As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line (Fig. 3–67) until she reaches the child at a point downstream. If the lifeguard can swim at a speed of 2.0 m/s relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child?
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(II) Two cars approach a street corner at right angles to each other (Fig. 3–57). Car 1 travels at a speed relative to Earth v₁ₑ = 35 km/h, and car 2 at v₂ₑ = 55 km/h . What is the relative velocity of car 1 as seen by car 2? What is the velocity of car 2 relative to car 1?
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(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.)