4. 2D Kinematics

Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent's speed relative to Susan's reference frame?

A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s. How long will it take him to cross?

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30° west of north while ship B travels 20° east of north at 25 mph. What is the speed of ship A as seen by ship B?

While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

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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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?

(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 v_T, 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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(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), how far from its intended position it will be after 11.0 min if the pilot takes no corrective action. [Hint: First draw a diagram.]

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

A person going for a morning jog on the deck of a cruise ship is running toward the bow (front) of the ship at 2.5 m/s while the ship is moving ahead at 8.8 m/s. What is the velocity of the jogger relative to the water? Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?