A motorboat crosses a river that is 130 m wide. The river runs north to south an

Question

A motorboat crosses a river that is 130 m wide. The river runs north to south and has a constantspeed of 5.50 m/s. The speed of the motorboat relative to the water is 17.5 m/s. In parts (a) to (e), assumethat the boat is aimed directly across the river (i.e., toward the east). (a) Draw a vector diagram representingthe velocity of the boat relative to the water, the velocity of the water relative to the earth, and the velocityof the boat relative to the earth. (b) Write the vector equation corresponding to the diagram in part (a).(c) What is the magnitude and direction of the velocity of the boat relative to the earth? (d) How long doesthe boat take to cross the river? (e) How far south does the boat travel while crossing the river? (f) Whatangle should the boat be aimed at to reach a point across the river directly opposite the launch point

Explanation / Answer

Draw the river as two vertical lines.

Direct north as the top of the page.

Speed of the river is denoted as 5.50m/s towards the bottom of the page.

The speed of the boat is 17.5m/s across the page left to right.

Connect the triangle (NW to SE) and this is answer A.

Vector equation (B) is:

speed of the boatrelative to land=speed of the boatacross the water+speed of waterrelative to land

Magnitude and direction can be found from the triangle.

Magnitude=(17.52+5.52)0.5=18.34m/s

Direction=tan-1(5.5/17.5)=17.45o South of East.

River is 130m wide, boat moves 17.5m/s horizontally. 130/17.5=7.43seconds

Distance southbound =7.43s*5.5m/s=40.86m.

Angle = 17.45o North of East.

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