6. The sides of a right triangle are measured to be a = 7.80 ± 0.02 cm and b = 6.40 ± 0.02 cm. Determine the length of the hypotenuse of the triangle (given by ?^2 +?^2 = ?^2) and the uncertainty in the length. (Hint: you need to use the derivative equation to find the uncertainty.)
7. If you drive 146 miles in a time of 3.25 hours, what is your average speed in km/h and m/s? How long would it take to travel an additional 175 km at this average speed?
6) Given,
A = 7.80 ± 0.02 cm
B = 6.40 ± 0.02 cm
A^{2} / A^{2} = A / A + A / A
A^{2} / A^{2} = 0.02 / 7.80 + 0.02 / 7.80
A^{2} / A^{2} = 0.005128
A^{2} = 0.005128 A^{2}
Similarly
B^{2} / B^{2} = B/ B + B / B
B^{2} / B^{2} = 0.02 / 6.40 + 0.02 / 6.40
B^{2} = 0.00625 B^{2}
Therefore,
A^{2} = 60.84 +/- 0.31198 cm^{2}
B^{2} = 40.96 +/- 0.256 cm^{2}
Now,
C^{2} = A^{2} + B^{2}
C^{2} = 101.8 +/- 0.56798 cm^{2}
fractional uncertainty in C^{2} is
C^{2} / C^{2} = 0.56798 / 101.8
C^{2} / C^{2} = 0.005579
C / C = 0.0027895
C = 0.0027895 * 10.089
C = 0.028145
Therefore,
C = 10.089 +/- 0.02814
-----------------------------------------------------------------------------------------------------------------
7) 1 mile = 1.60934 km
so,
146 miles = 234.964 km
so,
average speed = 234.964 / 3.25
average speed = 72.296 Km/h
In miles/sec
average speed = 146 / 11700 = 0.0125 miles / sec
time taken to travel additional 175 km
time = distance / speed
time = 175 / 72.296
time = 2.42 hours
6. The sides of a right triangle are measured to be a = 7.80 ± 0.02...
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