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A spacecraft flying in a straight course with velocity of 75 km/s fires its rocket motors for 6.0s. At the end of this time its velocity becomes 120 km/s . Find the distance travelled by the spacecraft in the first 10 s after the motors were started,the motors being in action for only 6.0s

Asked by Adrija 21st February 2018, 6:50 PM
Answered by Expert
Answer:
A spacecraft flying in a straight course with velocity of 75 km/s fires its rocket motors for 6.0s. At the end of this time its velocity becomes 120 km/s . Find the distance travelled by the spacecraft in the first 10 s after the motors were started,the motors being in action for only 6.0s

begin mathsize 12px style straight u equals 75 space km divided by straight s
straight v equals space 120 space km divided by straight s
straight t equals space 6 space secs
using
straight v equals straight u plus at
straight a equals fraction numerator straight v minus straight u over denominator straight t end fraction
straight a equals fraction numerator 120 minus 75 over denominator 6 end fraction
straight a equals 7.5 space km divided by straight s squared
using
straight v squared equals straight u squared plus 2 as
straight s equals fraction numerator straight v squared minus straight u squared over denominator 2 straight a end fraction equals fraction numerator 120 squared minus 75 squared over denominator 2 cross times 7.5 end fraction equals 585 space km
assuming space that space after space 6 space seconds comma space the space rocket space stops
and space being space in space space space and space due space to space inertia space it space continued space
to space move space at space straight a space constant space velocity space of space 120 space km divided by straight s
Thus space after space 6 space seconds comma space the space rocket space travels space for space 4 space more space seconmds
that space distance space is space equals space 120 space cross times space 4 space equals space 480 space km

Thus space total space distance space travelled space by space rocket space for space 10 space seconds space equals space 585 plus 480 equals space 1065 space km end style
Answered by Expert 21st February 2018, 7:28 PM
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