(8%) Problem 10: explores a shallow reef off the coast of Belize. She initially swims d 1 = 78.3 m north, makes a tum to the east and continues for d2 = 153.9 m, then follows a big grouper (a kind of fish) for d3 = 85.9 m in the direction 0= 43.4° north of east. Finally, she swims d4 = 175 m south DA 50% Part (a) What is the straight-line distance between her initial and final positions in m? 1 R= m Grade Summary Deductions Potential 100% Late Work 96 100% sin() cos( tan() T ( 7 8 9 HOME Late Potential 100% cotan() asin() acos() E 5 6 1 atan() acotan() sinh() 2 3 Submissions Attempts remaining: 999 (0% per attempt) detailed view cotanh() cosh() tanh() ODegrees O Radians Submit Hint Hints: 0% deduction per hint. Hints remaining: 1 A E O a d d ed ed ch n 1 4 1 → 14 0 END NO BACKSPACE m CLEAR Feedback I give up! Feedback: 0% deduction per feedback. (99+ 14 W ((?) 69°F 096 12:14 AM E 5/25/2022

An airplane with a ground speed of 450 m/s, heading due south. A gentle wind blowing at 18 km/hr having an angle of 60° from the bearing. (i) Sketch the scenario with proper diagram and compute: (ii) the true air speed (iii) Find heading direction of the airplane from north.

A woman can row a boat at 7.60 km/h in still water. (a) If she is crossing a river where the current is 3.80 km/h, in what direction must her boat be headed if she wants to reach a point directly opposite her starting point? Express your answer as an angle with respect to the line perpendicular to the river, positive if down the river. (b) If the river is 7.60 km wide, how long will she take to cross the river? (c) Suppose that instead of crossing the river she rows 3.80 km down the river and then back to her starting point. How long will she take? (d) How long will she take to row 3.80 km up the river and then back to her starting point? (e) In what direction should she head the boat if she wants to cross in the shortest possible time, and (f) what is that time?

What will be the speed of an airplane that normally flies at 200km/h when it encounters a 80km/h wind from the side( at the right angle to airplane)?

7) The water in a river flows uniformly at a constant speed of 2.50 m/s between parallel banks 80.0 m apart. You are to deliver a package across the river, but you can swim only at 1.50 m/s. a) If you choose to minimize the time you spend in the water, in what direction should you head? b) How far downstream will you be carried? c) If you choose to minimize the distance downstream that the river carries you, in what direction should you head? d) How far downstream will you be carried? (a: straight across, b: 53.3 s and 133 m downstream, c: 36.9 degrees, 107 m)

(a) A physicist runs straight south at velocity 8 mi/hr. She decides to change her course so that the wind is at her back (directly from the north, relative to the earth) at velocity 20 mi/hr. She decides to change her course so that the wind will striker her right side (i.e., at 90° relative to her motion). By what angle must she change her direction of motion?

A Polynesian boater leaving Vanunu wishes to make landfall on an island 210Km directly south. She can paddle at 5.4 Km/Hr (relative to the water) but there is a gentle ocean current flowing 37 degrees east of due south. She compensates for that by pointing her craft at 7.8 degrees west from due south. A) How fast is the current flowing? B) How long (hours) does her journey take?

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In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.50 km 45.0º north of west; then 4.70 km 60.0º south of east; then 1.30km 25.0º south of west; then 5.10 km straight east; then 1.70km 5.00º east of north; then 7.20 km 55.0º south of west; and finally 2.80 km10.0º north of east. What is his final position relative to the island?