Question

1.Suppose you are trying to cross from the South bank to the North bank of a river in your covered wagon. With all your earthly possessions, you are able to move your wagon at a speed of 1.3 m/s with respect to the water. The crossing is normally perfectly safe, but it’s been a warm spring and the snow melt is causing the river to swell to 20.0 m wide and to flow quickly at 1.0 m/s to the west.a)In what direction do you need to aim your wagon if you want to cross the river without drifting downstream or upstream? How quickly will you cross the river in this case?b)In what direction do you need to aim your wagon if you want to cross the river in the shortest amount of time? How long will it take you to cross in this case?

2.It is raining outside. From the perspective of an observer standing on the ground, the raindrops are falling vertically downward at a speed of 12 m/s. You are driving down the highway at a speed of 65 mph (29 m/s). What angle, relative to the horizontal will you see the raindrops falling?

Answer 1

Date: Part 1) what direction should wagon be aimed at straight Northward. as it mores ↑ Vresultant A wagon (direction will be in terms of North of East (0) Vriver N wagon) A E Ļ sino East of North (90-0) w s Vriver COS wagon COSO Vriver 0 = 39.7° 1 1.3 wagon Angle is 39.7° [ direction 39.7° 50.3 North of East East of North. Part 2) How quickly you cross the river Uwagen sino 103 sin 39.7 "0.83 mis Part 3) Shortest time time = Dislence speed when you Northwards ie perpendicular to flow of river, om wagon straight speed maximises Teacher's Signature NAVEL

so wagon should be cimed straight Northwards Part 4) Time taken ( shortest ) wagon Vresullem o 20 m D o Vresultent = 1-31+12 1.64 m/s DE 20 coso dislemce = 2 $.23 m o = tan 20 cose tan! ( 113 ) Cos 0 = 1.3 Time 95, 23 1-64 115.38. sec 1.64 10 - 1.3 → 29 m/s 2 12 m/s 29 K 21 tamo = 12 29 12 You 05 22.50