Question

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?

Answer 1

6) Given,

A =  7.80 ± 0.02 cm

B = 6.40 ± 0.02 cm

$\Delta$A² / A² = $\Delta$A / A + $\Delta$A / A

$\Delta$A² / A² = 0.02 / 7.80 + 0.02 / 7.80

$\Delta$A² / A² = 0.005128

$\Delta$A² = 0.005128 A²

Similarly

$\Delta$B² / B² = $\Delta$B/ B + $\Delta$B / B

$\Delta$B² / B² = 0.02 / 6.40 + 0.02 / 6.40

$\Delta$B² = 0.00625 B²

Therefore,

A² = 60.84 +/- 0.31198 cm²

B² = 40.96 +/- 0.256 cm²

Now,

C² = A² + B²

C² = 101.8 +/- 0.56798 cm²

fractional uncertainty in C² is

$\Delta$C² / C² = 0.56798 / 101.8

$\Delta$C² / C² = 0.005579

$\Delta$C / C = 0.0027895

$\Delta$C = 0.0027895 * 10.089

$\Delta$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