A kayaker can paddle her kayak at a steady 2.5m/s in still water. She wishes to

Question

A kayaker can paddle her kayak at a steady 2.5m/s in still water. She wishes to cross a river that is 2000m wide and has a current of 1.5m/s.

(a) IF the kayaker first "aims" her craft straight across the river, the current will carry her downstream as she paddles across. What will be her actual velocity (magnitude and direction angle) as she crosses? How long will it take her to cross the river?

(b) If she "aims" the kayak somewhat upstream, she can actually travel straight accross the river. In what direction must she aim? What is her actual speed accross the river for this situation, and how long will it take her to cross?

Please note that we must use cartesian angles and not polar. HINT: The angle found in (a) will NOT be the same angle required in part (b). --- I have figured out (a) to be: a velocity of 2.92 m/s at 329 degrees (CCW from x axis). It would take 686s to cross. Is that right? And could someone help me on (b) please? :)
Please note that we must use cartesian angles and not polar. HINT: The angle found in (a) will NOT be the same angle required in part (b). --- I have figured out (a) to be: a velocity of 2.92 m/s at 329 degrees (CCW from x axis). It would take 686s to cross. Is that right? And could someone help me on (b) please? :)

Explanation / Answer

Given Width of the river,s = 2000 m a)velocity of water relative to ground, Vwg = 1.5 m/s velocity of boat relative to water, Vbw = 2.5 m/s velocity of boat relative to ground, Vbg is       Vbg = Vbw +Vwg             = (2.5 m/s) j+ (1.5 m/s)i      magnitude of Vbg = v(2.5)^2+(1.5)^2                                = 2.91 m/s Thus the actual velocity is 2.91 m/s Direction, ? = tan^-1(2.5/1.5)                 ? = 59^0 with respect to x axis ----------------------------------------------------------------------------------- The time to cross the river is t =2000 m/(2.91 m/s) t = 687.28 s or 11.45 min -------------------------------------------------------------------------------------- b) If she would row the boat upstream, then the velocity of boat is     v = Vbw - Vwg     v = 2.5 m/s -1.5 m/s = 1.0 m/s    Direction ? = tan^-1(2.5/-1.5) = 149 ^0 counter clock wise from x axis    towards north west    Time taken to cross the river with velocity 1.0 m/s             t = 2000 m/(1.0 m/s)               = 2000 s or 33.33 min

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.