3. a. 4 pts. A motorboat\'s bow is pointed due south. and its motor gives the bo

Question

3. a. 4 pts. A motorboat's bow is pointed due south. and its motor gives the boat a constant speed of 650 m/s through still water. However, the water has a current flowing due east at a speed of 300 m/s. Find the magnitude a and direction of the boat's total velocity (relative to stationary objects along the shore). Show your work. Include a sketch of the two velociry vectors and their suwn, b. 3 pts) f the boat and water current maintain these same velocities for 60.0 seconds. find the magnitude and direction of the boat's displacement. Show your work completely. BONUS: (+2 pts.) suppose that the boat captain is traveling through the same flowing water, but wants to have the boat's total velocity be directed dur sowth. (The boat's molor-speed through stationary water is still 6.50 m/s, and he water's current is still 3.00 m/s due east J. At what direction should the captain aim the bow of the boat? (Specify rhe exact angle for your final direction, not just "southwest.") You do NOT need to show voter work. direction ain. What will be the magnitude of the boat's total velocity in this case? Your do NOT need to show your work. Include units on your answer! total velocity

Explanation / Answer

magnitude = sqrt [6.52 + 32]

= 7.16 m/s

theta = tan-1 [6.5 / 3]

= 65.22 deg

----------------------------------------------

displacement = velocity * time

= 60 * (3i + 6.5 j)

= 180 i + 390 j

|D| = 429 m

theta = tan-1 [6.5 / 3] = 65.22 deg

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