How Do You Calculate Acceleration in Space Probe Motion Problems?

[efaizan]

college phys 1111... neeed help!

Homework Statement

A space probe is desperately trying to escape the gravitational pull of a massive planet. After a final blast of its thrusters, the probe has a velocity of 2940 m/s away from the planet. Later, the probe is 176.4 km closer to the planet than it originally was, with a velocity of 8820 m/s toward the planet.

You are to find (assume constant acceleration):
a) the acceleration (magnitude and direction)
b) How far beyond its starting point the probe got.
c) How much time elapsed between initial and final positions.

I don’t understand how to approach this problem…. How do I find acceleration when I don’t know the time?

 

[ideasrule]

You know that the probe's velocity was originally 2940 m/s, but that after falling 176.4 km towards the planet (and losing a corresponding amount of potential energy), its velocity became 8820 m/s. You can use the conservation of energy to calculate g, the acceleration due to gravity.

For b, you can use the conservation of energy again. c should be easy once you get the answer for a.

 

[efaizan]

i am sorry i still don't understand... =[

 

[efaizan]

i mean i know (Velocity final- Velocity initial)/time = acceleration but they don't tell the time and that is what is throwing me off...

 

[Redbelly98]

How do I find acceleration when I don’t know the time?

Look at the kinematic equations for motion with constant acceleration. Look for the one equation that does not contain time t.

 

[efaizan]

v^2=vo^2+2a(x-xo) or

 

[efaizan]

v^2-vo^2=2a(x-xo)

 

[efaizan]

2940^2-8820^2=2a(x-176.4) and solve for a?

 

[Redbelly98]

Yes. Um, you do know what the value of x is, right?

 

[efaizan]

ummm 0?

 

[ideasrule]

Yup, exactly. But you used 176.4, which is in kilometers, whereas all your speeds are in m/s. You'll have to make the units agree.

 

[efaizan]

ok so 2940^2-8820^2=2a(0-109.6) i got a= 315459.85... that doesn't sound right does it?

 

[efaizan]

thank you guys btw for ur help!

 

[Jebus_Chris]

Well first convert x into meters, there are 1000 meters in 1km. Know you just plug and chug. And for some odd reason you have Vo as 8820 and V as 2940.

 

[efaizan]

ohhhh oops i think i converted the 176.4 km to miles... soooo i should flip flop the v's? and 176.4 km to meters would be 176400?

 

[efaizan]

ok so i did it again and i got 196 for a now... that sounds kinda right. right?

 

[Jebus_Chris]

Looks good.