Solution 51E

Step 1

(a) The acceleration of the rocket is given by

 …. (1)

Integrating equation (1) with respect to  we have

 … (2)

Here  is the constant of integration. Now, we know that the rocket is starting from rest. Hence the initial velocity zero, so we have at , , putting the value in above equation we have

So, equation (2) becomes

 … (3)

Again integrating the equation (3) with respect to  we get

 … (4)

Here  is the constant of integration. Again we know that the rocket starts from the surface of the earth. Hence the displacement is zero at , using this value in equation (4), we can write that

Hence the displacement at any time  is given by

 … (4)

Now putting the value of  we have

At  the height of the rocket is 2133 m.