Question
In gravity -free space, a spaceship fires its rockets to speedup. The rockets are programmed to increase thrust from zero to 1.00x 10^4 N with a linear increase over the course of 18.0km. Then thethrust decreases linearly back to zero over the next 18.0km.Assuming the rocket was stationary to start,a). During whichsegment will more work ( magnitude) be done.(1)the 1st 60 seconds,(2) the 2nd 60 seconds, (3) the work done is the same in bothsegments? Explain the reasoning. b) determine quantitatively how much work is done in eachsegment. In gravity -free space, a spaceship fires its rockets to speedup. The rockets are programmed to increase thrust from zero to 1.00x 10^4 N with a linear increase over the course of 18.0km. Then thethrust decreases linearly back to zero over the next 18.0km.Assuming the rocket was stationary to start,a). During whichsegment will more work ( magnitude) be done.(1)the 1st 60 seconds,(2) the 2nd 60 seconds, (3) the work done is the same in bothsegments? Explain the reasoning. b) determine quantitatively how much work is done in eachsegment.
Explanation / Answer
velocity of the rocket by the time it is at end ofsegment S= at^2/2 t = time ofjourney S = 18km a = F / m F = 1.00* 10^4 N from abv relation we can sovle for time of travell over18km height and final velocity by the time it cross firstsegment V =at Work done on the rocket in time ' t ' W = mV^2 / 2 m = mass of the rocket . time of travell for the second segment S = v't-gt^2 / 2. S = 18km v' = velocity at the end of thefirst segment g = accleration due togravtiy frm this relation we can solve for velocity at the endof second segment and work done W' = mv'^2 / 2 pluging the known values we can solve for velocityW' .