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## Homework Statement

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Over 40 years ago, the Apollo astronauts placed reflectors on the surface of the Moon. These are still used by a number of observatories on Earth to monitor the distance to the Moon by reflecting pulses of laser light from them and detecting the reflected signal. Scientists have determined that the Moon is at a distance of 363104 km at its closest and 405696 km at its furthest. It has also been determined that the Moon is getting about 3.8 cm further away from the Earth each year.

(a) Describe how the reflected pulses can be used to determine the distance to the Moon. (2)

Ans a- (already done) d = (s * t) / 2, where s is the speed of light and t is time for return trip.

(b) An observatory sends out pulses of laser light of duration 2.0 × 10^-10 s when it is determining the distance to the Moon.

(i) Calculate the pulse length. (2)

Ans b(i)- (already calculated) 0.06m or 6cm

(ii) Discuss whether the levels of precision quoted for the distance to the Moon and its rate of increasing distance from the Earth are justified. (2)

Ans b(ii)- (cannot understand)

## The Attempt at a Solution

markscheme(ms):

Distance is to the nearest km but pulse length is to the nearest mm, so acceptable (accept pulse length to nearest cm) (1)

Not acceptable because 6.0 cm pulse is longer than 3.8 cm, Or The distance is calculated from a difference over 40 years, so it is over a metre, so it is acceptable compared to 6.0 cm (1)

examiners report(er):

Few students scored on this question. Many focused on significant figures, missing the point that using a pulse a few centimetres long justifies quoting an answer to the nearest kilometre despite there being 6 significant figures in the kilometre value. They did not realise that the uncertainty should be less than the quoted value, or link the length of the pulse with uncertainty at all.

I looked into these after failing to understand the question. The answer i wrote was completely wrong.

My answer: The distances are in km while the answer in cm. Then i calculated the % increase of distance to the moon using the rate of increasing distance from the Earth for some reason.

405696 * (100.000038/100) = 405696.15

(0.154/405696) * 100 = 3.8 * 10^-5 increase so not justified

Completely wrong. After reading the ms and er i still dont understand this question.

Please help.