Rocket Height as one-dimension motion

[popxel]

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t1, when the fuel is exhausted.

Find the maximum height H that the rocket reaches (neglecting air resistance).

Express the maximum height in terms of a, t1, and/or g. Note that in this problem, g is a positive number equal to the magnitude of the acceleration due to gravity.

That's part 1. Then comes:

If the rocket's net acceleration is a=3g for t1=5.00 s, what is the maximum height the rocket will reach? (Using 9.81 m/s^2 for g).

 

[mukundpa]

Please first of all show your work.

 

[quicknote]

I would approach this problem by first defining the variables and equations that relate to the motion of the rocket. In this case, the key variables are acceleration (a), time (t), and height (H). The relevant equation for one-dimensional motion is H=1/2at^2, where a is the acceleration and t is the time.

To find the maximum height, we can use the equation H=1/2at1^2, as this represents the height at time t1 when the fuel is exhausted. Plugging in the given values of a and t1, we get H=1/2(3g)(5.00 s)^2=37.125 m.

This means that the maximum height the rocket will reach is 37.125 meters. We can also express this in terms of g by substituting the value of g (9.81 m/s^2) into the equation, giving us H=1/2(3)(9.81 m/s^2)(5.00 s)^2=147.105 m.

In conclusion, the maximum height the rocket will reach is 37.125 meters or 147.105 meters, depending on whether we use the value of a in terms of g or not. This calculation assumes that there is no air resistance, which would affect the motion of the rocket and therefore the maximum height it can reach.