1. The downward vertical position of a ball released from rest on Earth is measu

Question

1. The downward vertical position of a ball released from rest on Earth is measured to be 0,5,18,40 in meters at times t = 0.000,1.000,2.000,3.000 s. The estimated standard error for each of the height measurements is 0.5 m and these errors are assumed to be independent of each other. Are the measurements consistent with vanishing drag? Why or why not?

2.  A space craft travels away from an inertial observer with = 10. A tail light on the craft ashes at a rate of 1 Hz according to the pilot. At what rate are pulses received by the observer when the craft is at a distance of 1 light-year? (Assume the pulses are bright enough to be detected.)

Explanation / Answer

1. given, data

time position

0 0

1 5

2 18

3 40

by plotting this data on excel the equation of the data is

y = 4.25t^2 + 0.55t + 0.05

hence, comparing this with y = yo + ut + 0.5at^2

acceeleration due to gravity = 8.5 m/s/s

this value of the acceleration due to gravity increases to 9 m/s/s if only last 3 points are used

hence the acsceleration due to gravity is getting closer to the actual value so the measurements are consistent with vanishing drag

2. given, gamma = 1/sqroot(1 - v^2/c^2) = 10

0.01 = 1 - v^2/c^2

0.99498c = v

frequency of the tail light, fo = 1 Hz

let the apparent frequency be f

then from relativistic doppler's effect

observed frequency f = sqroot([1 - 0.99498]/[1 + 0.99498])fo = 0.002516 Hz

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