A rocket starts from ground from rest with an acceleration...

A rocket starts from ground from rest with an acceleration of 10.0 m/s2 and is expected to move upwards for 40 seconds a) What will be the maximum height it will reach after 40 s? b) What is the expected velocity at 40 s c) If instead, it loses the fuel after 20 seconds of takeoff, does the rocket move up or down immediately after the fuel exhausted d) What is the magnitude and direction of rocket’s acceleration immediately after the fuel exhaustion e) How long does it move up after losing fuel f) What is the max. distance it travels before falling g) How long is it in air totally before falling to the ground

Transcript

00:01 Hello, here a rocket rises vertically from the rest with acceleration of 3 .2 meters per second squared until it runs out of fuel at an altitude of y1, which is 795 meters.

00:16 First, we have to find the velocity of the rocket when it runs out of the fuel, we won.

00:22 Let's here illustrate y axis switches up.

00:26 So the rocket starts from zero.

00:28 At y1, it gets rid of the fuel.

00:32 And at this point it has a velocity of v1 and after this point the rocket travels under acceleration of g so this v1 can be found as following so the coordinate y1 equals to v1 squared minus 0 squared divided by 2a1 therefore v1 equals to square root of 2a1 times y1 which is square root of 2 times 3 .2 meters per second squared times 795 meters let's calculate it that is 71 .3 meters per second which is roughly 71 meters per second now let's answer question b we have to calculate how long it will take to reach this point and this times t1 equals to v1 divided by a1 that is 71 let's take more scientific figures for better precision divided by 3 .2 meters per second squared and now let's answer it so that is 22 .3 seconds which is roughly 22 seconds now let's answer question c here we have to calculate maximum altitude and maximum altitude equals to y1 plus v1 squared divided by 2g that is 7295 meters plus 71 .3 meters per second squared divided by 2 and 9 .8 meters per second squared that is 1 ,055 ,000 ,000, yeah ,000 and 1 ,000 and 55 meters.

03:09 Now let's answer question d where we have to calculate how much, how long it will take to reach the maximum altitude.

03:25 So this time which is needed to reach maximum height equals to t1 plus v1 divided by g which is 22 .3 seconds plus 71 .3 meters per second divided by 9 .8 meters per second squared.

03:53 So let's calculate it.

04:01 That is 29 .6 seconds, which is roughly 30 seconds.

04:08 Now let's answer question e.

04:10 Here we have to calculate with which velocity is twice...

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