There is a proposal in brooklyn to construct a new mid-rise apartment building on a vacant lot at the intersection of avenue a and 48th street. the property is square, providing flexibility for the location of the building and an associated playground. the developer wishes to locate a small park and playground adjacent to the quietist street. the traffic volumes for avenue a are: cars – 496; medium trucks – 52, heavy trucks – 19; and buses - 10. the traffic volumes for 48th street are: cars – 822; medium trucks – 22, heavy trucks – 8; and buses - 3. following his thinking, which street should the park be adjacent to? (3 points) assuming the setbacks are the same, what is the difference in noise levels adjacent to the 2 streets? (4 points) based upon people’s perceptions of noise differences, are the developer’s concerns valid? why? (3 points)
answer & explanation:
"the force on a cutting tool are 2600n vertically downward" sounds a little unusual, since most of the time, the tool is above the object to be cut in such a way that the force acting "on the tool" is upwards. we will accept the statement as it is (downwards).
since the two forces are acting at right angles to each other, the resultant can be found using pythagoras theorem, namely
resultant = sqrt(2600^2+2100^2) = 3342 n (approx.)
the angle can be found using the arctangent function, or
angle = arctangent(2600/2100) = 51.07 degrees below the horizontal, since the 2600 n force is acting downwards.
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