Determine when (m), and how long the rocket should fire.

[pnstu]

Homework Statement

Your job is to determine when the lunar lander should fire its rocket to reduce its landing speed to below 5m/s for a safe landing. The lander will descend to the moon from an orbit 1000 meters above the surface of the moon (acceleration = 1.625 m/s^2). To avoid crashing into the surface, the lander has a rocket that can fire up to 10 seconds and provide upward acceleration at 25m/s^2. Determine when (in meters) and how long the rocket should fire to reduce the landing speed to below 5m/s.

Relevant Equations

AP Physics 1 Kinematic Equations
vf=vi+at
xf=xi+vi(t)+1/2(a)(t^2)
vf^2=vi^2+2a(xf-xi)

Homework Statement: Your job is to determine when the lunar lander should fire its rocket to reduce its landing speed to below 5m/s for a safe landing. The lander will descend to the moon from an orbit 1000 meters above the surface of the moon (acceleration = 1.625 m/s^2). To avoid crashing into the surface, the lander has a rocket that can fire up to 10 seconds and provide upward acceleration at 25m/s^2. Determine when (in meters) and how long the rocket should fire to reduce the landing speed to below 5m/s.
Homework Equations: AP Physics 1 Kinematic Equations
vf=vi+at
xf=xi+vi(t)+1/2(a)(t^2)
vf^2=vi^2+2a(xf-xi)

Apologies if this is posted in the wrong section

What I've gathered from the givens is that

ΔX=1000m
a(moon)= 1.625m/s²
total time the rocket can be activated=10s
a(rocket)=25ms/s²

I am completely lost on how to start this.

 

[BvU]

Hello pnstu, !

I am completely lost on how to start this

Not good enough -- see PF guidelines

Fortunately you have some good equations in your toolkit, so fill in a few knowns like v_i, v_f, x_i, x_f and think what you would do if you were at the controls and don't want to crash: fire right away ? Not a good idea. So yout height as a function of t will be free fall at first.

Comment from me: nothing is said about the initial orbit, so I gather you are allowed to assume you start out just hanging up there at 1000 m above the moon and start to fall[edit] Oh, and use the Subscript button

 

[anorlunda]

I used to have a lunar lander game on my computer. To win the game, you had to solve this exact problem, but not using calculations, but using a joystick.