Far in space, where gravity is negligible, a 435 kg rocket...

Far in space, where gravity is negligible, a 435 kg rocket traveling at 75.0 m/s in the positive x-direction fires its engines. The figure (Figure 1) shows the thrust force as a function of time. The mass lost by the rocket during these 30.0 s is negligible. Part A What impulse does the engine impart to the rocket? Express your answer in newton seconds using two significant figures. Jx = N · s Part B At what time does the rocket reach its maximum speed? Express your answer in seconds using two significant figures. t = s Part C What is the maximum speed? Express your answer in meters per second using three significant figures. Figure Fx (N) 1000 0 0 10 20 30 t (s)

Transcript

00:01 In this question, it is given that the mass of rocket is m equal to 435 kg and it is traveling at a speed of, that is, initial speed equal to 75 .0 meter per second along the positive x direction.

00:27 And the figure that is a force versus time graph is given here.

00:36 Force fx versus time graph and we need to consider the mass lost by the engine during the 30 second that is t equal to 0 seconds from 30 .0 second is 30 .0 second is negligible so no mass is lost from 0 to 30 seconds and first question for support support support we need to find the inverse does the engine import to the rocket so jx that can be written as fx times t or the inverse inverted to the rocket that can be written as the area under the force fx versus time graph so here the graph the shape of the graph is a triangle we need to find the area of the triangle that is consider this as a this is p and this is c also the height of the triangle that is this one consider this point as d so we can write the area of triangle that is half base into height base is ac and height is bd so we can substitute the values to find the impulse that's the engine impart to the rocket so half times ac that is 30 second and b d that is height of the triangle that is thousand newton so we can calculate the impulse inverted to the rocket as 1 ,500 newton second.

02:50 For part b, it is asked to find at one time does the rocket reach its maximum speed? here from the given graph, the speed of the rocket keeps on increasing.

03:12 Increasing as the acceleration acting on the rocket becomes zero.

03:34 We know that it is already given in the graph itself.

03:39 The force acting on the rocket becomes zero when time t equal to 30 seconds.

04:01 Therefore the time at which the rocket reaches maximum speed, that is, t equal to 30 second.

04:11 And part c is asked to find the maximum speed of the rocket so from the definition of imbalts we can write j x that is equal to fx times t what is force force is the product of mass times the acceleration so it can be written as m times a x times t so we know that acceleration is the rate of change of velocity...

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