You are sending a radio signal from your rocket to mission control on Earth. You

Question

You are sending a radio signal from your rocket to mission control on Earth. You send wavelength 6.1 cm and are going at a speed of -8.5km/sec relative to mission control. How different is the wavelength received by mission control from the wavelength you sent? Give your answer in scientific notation to two significant figures. Express the answer in cm and be sure to include the sign of the answer (plus or minus) and compute the answer to two significant figures (so two digits, but NOT including leading or trailing zeros)

Student response: 23
Correct answer: -1.7E-4 (-1.7 * 10-4)
General feedback: Hint, you are calculating change in wavelength
Score: 0 / 1

An asteroid orbits the Sun in circular orbit at a distance of 4.6 AU. How fast would it need to be going to escape from the Sun? Give your answer in km/sec to the nearest .1 km/sec. Remember that objects orbit the Earth in low Earth orbit at 7.8 km/sec and the Earth orbits the Sun at 30 km/sec.

Student response: 23
Correct answer: 19.8
Score: 0 / 1
An asteroid orbits the Sun in circular orbit at a distance of 0.9 AU. How fast is it going? Give your answer in km/sec to the nearest .1 km/sec. Remember that objects orbit the Earth in low Earth orbit at 7.8 km/sec and the Earth orbits the Sun at 30 km/sec.

Student response: 13
Correct answer: 31.6
Score: 0 / 1

Explanation / Answer

1) So, since the speed given is much less than the speed of light, you can use the approximation that:
/ v/c

You're looking for , so it's just going to be v*/c. Since v and c are of the same units, you don't have to worry about the units on them, as long as they cancel

(6.1cm)*(8500m/s)/(3*10^8 m/s) = 1.73*10^-4 cm

2) So the necessary condition for something to achieve escape velocity is for its potential energy to equal the kinetic energy associated with the velocity it's going. So using that you can find the escape velocity with:

.5mvesc2= GmMsun/r

.5vesc2= GMsun/r

Vesc = (2GMsun/r)

Vesc = (2*(6.67*10^-1)*(2*10^30kg)/(4.6*1.5*10^11) = 19863 m/s = 19.8 km/s

3) Same deal as above, except in this case we're equating the centripetal force (which we can use because it's a circular orbit) with the gravitational force:

mastv2/r = GmastMsun/r2

v2 = GMsun/r

v = (GMsun/r)

=(6.67*10^-11*2*10^30/(.9*1.5*10^11)) = 31634 m/s = 31.6 km/s

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