Question

Future space rockets might propel themselves by firing laser beams, rather than exhaust gases, out the back. The acceleration would be small, but it could continue for months or years in the vacuum of space. Consider a 1200 kg uncrewed space probe powered by a 15 MW laser. After one year, how far will it have traveled and how fast will it be going

Answer 1

Answer:

Acceleration = 0.0282 m/s^2

Distance = 13.98 * 10^12 m

Explanation:

we will apply the energy theorem

work done = ΔK.E ( change in Kinetic energy )  ---- ( 1 )

where :

work done = p * t

                  = 15 * 10^6 watts * ( 1 year ) = 473040000 * 10^6 J

( note : convert 1 year to seconds )

and ΔK.E = 1/2 mVf^2   given ; m = 1200 kg  and initial V = 0

back to equation 1

473040000 * 10^6  = 1/2 mv^2

Vf^2 = 2(473040000 * 10^6 ) / 1200

∴ Vf = 887918.92 m/s

i) Determine how fast the rocket is ( acceleration of the rocket )

a = Vf / t

  = 887918.92 / ( 1 year )

  = 0.0282 m/s^2

ii) determine distance travelled by rocket

Vf^2 - Vi^2 = 2as

Vi = 0

hence ; Vf^2 = 2as

s ( distance ) =  Vf^2 / ( 2a )

                     = ( 887918.92 )^2 / ( 2 * 0.0282 )

                    = 13.98 * 10^12 m