Question

Plzzz show your work neatly, i have problem reading other people's handwrittings. Thanks :)

A river flows due south with a speed of 4.5 m/s. A man steers a motorboat across the river. His motor can push the boat through water at a speed of 7 m/s. Starting on the western shore, he points the nose of his boat due east. The river is 500 m wide. What is his speed relative to the ground? 8. b. 3.95 m/s d. 10.3 m/s c. 6.22 m/s a. 8.32 m/s 9. What direction is he moving relative to the ground? d. 17.1° SE c. 21.6° SE b. 40.0° SE a. 32.3° SE 10. How much time is required to cross the river? c. 58.9 s d. 98.1 s b. 71.4 s a. 170 s 11. How far south of his starting point will he reach the opposite bank? b. 321 m d. 213 m c. 844 m a. 512 m 12. Later, the same boatsman using the same boat and starting again from the western shore wants to reach apoint on the opposite bank directly east of his starting point. In which direction should he head (i.e. which direction should he point the nose of his boat)? d. 17.1° NE b. 40.0° NE c. 21.6° NE a. 32.3° NE 13. What is the speed of his boat relative to the ground when he takes this heading? b. 4.11 m/s d. 5.36 m/s c. 7.91 m/s a. 1.97 m/s 14. How long will it take him to cross the river? d. 211 s b. 48.1 s c. 93.3 s a. 113 s

Answer 1

8] speed of boat relative to ground = sqrt(4.5^2+7^2) = 8.32 m/s option a

9] direction of movement = arctan(4.5/7) = 32.7 degree SE option a

10] time required t = d/v = 500/7 = 71.4 s option b

11] distance moved in south = vriver*t = 4.5*71.4 =  321m option b

12] His direction will be at angle which cancels rivers velocity

7*sin theta = 4.5

theta = arcsin(4.5/7) = 40 degree NE

option b

13] speed of his boat will have only east component = 7*cos 40 degree = 5.36 m/s option d

14] time taken = distance/speed = 500/5.36 = 93.3s option c