Finding initial speed given final speed

In summary, the radius of Mercury is 2440 km and its mass is 0.31024 kg. An object is launched straight up from just above the atmosphere and its initial speed needs to be calculated in order for its final speed to be 2500 m/s when it is far from Mercury. This is another conservation of energy problem that can be solved by considering the differences between solving for escape speed and starting speed when the speed at infinity is greater than zero.
  • #1
jamagner
5
0
The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg. An object is launched straight up from just above the atmosphere of Mercury.
(a) What initial speed is needed so that when the object is far from Mercury its final speed is 2500 m/s?

the second part is about the escape speed which i already figured out
 
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  • #2
This is another conservation of energy problem.
 
  • #3
jamagner said:
The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg.

Check your values, by the way. Mercury certainly has more mass than 0.3 kg...

What needs to be different about using conservation of energy to solve for the escape speed versus solving for the starting speed when the speed at infinity is greater than zero?
 
  • #4
dynamicsolo said:
Check your values, by the way. Mercury certainly has more mass than 0.3 kg...
:rofl: A typo, I presume. More like 0.3x10^24 kg.
 

What is the formula for finding initial speed given final speed?

The formula is v0 = v - at, where v0 is the initial speed, v is the final speed, a is the acceleration, and t is the time interval.

What units should be used when finding initial speed given final speed?

The units for initial speed and final speed are typically in meters per second (m/s). The units for acceleration are meters per second squared (m/s2), and the units for time are usually in seconds (s).

How do I determine the acceleration if it is not given?

If the acceleration is not given, you can use the formula a = (v - v0) / t, where a is the acceleration, v is the final speed, v0 is the initial speed, and t is the time interval. You can also use other equations, such as a = (2Δx - v0t) / t2, where Δx is the change in position and t is the time interval.

Can I use this formula for objects with non-constant acceleration?

Yes, you can use this formula for objects with non-constant acceleration. However, the calculated initial speed will only be accurate if the acceleration remains constant during the time interval t. If the acceleration changes, you will need to use more complex equations or estimates to find the initial speed.

Can I use this formula for objects moving in a curved path?

Yes, you can use this formula for objects moving in a curved path as long as the acceleration is constant. However, for objects with changing acceleration, you will need to use more advanced equations or estimates to determine the initial speed.

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