Unit: mechanics
Year: 1993 Question#: 9
Question: A boat heads directly eastward across a river at 12 meters per second. If the current in the river is flowing at 5 meters per second due south; what is the magnitude of the boat's resultant velocity?
(1 ) 7 m/s
(2 ) 8.5 m/s
(3 ) 13m/s
(4 ) 17m/s
What is this question really asking?
Explanation by: Lindsay K
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Answer 1
7 m/s
INCORRECT
You do NOT subtract 5m/s from 12m/s (12m/s - 5m/s = 7m/s THIS IS NOT WHAT YOU DO) Because these velocities are not acting in opposite directions. return to top
Answer 2
8.5 M/S
INCORRECT
You do NOT take the average of 12m/s and 5m/s (12m/s + 5m/s divided by 2 = 8.5m/s YOU DO NOT DO THIS) Try drawing a vector diagram. return to top
Answer 3
13 m/s
CORRECT
For this problem use the Pythagorean Therom: a2 + b2 = c 2
Plug numbers into the Pythagorean Therom:
(5m/s)(5m/s) + (12m/s)(12m/s)= (c)<sup>2</sup> 25m2/s2+144m2/s2=(c)2 169m2/s2 = (c)2 13m/s=c
You can use a picture to help you. Draw in the directions of the forces, into a
right triangle and add the proper numbers. See the diagram above.
return to top Answer 4
17m/s
INCORRECT
You do NOT add 12m/s and 5m/s together (12m/s +5m/s = 17m/s YOU DO NOT DO THIS ). The boat's resultant velocity is a vector sum not an ordinary sum. Remember, direction matters. return to top
What's this question really asking?
How do you apply the Pythagorean Theorem to find the vector sum of vectors acting concurrently? return to top
