- #1

sander2798

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the problem I have to solve is as following.

*You're in space and you're moving with a constant speed. Now, you want to accelerate. For this you will be using Newton's third law.*

Xenon 1+ iones will be shot from the back of the spacecraft with high speeds, the avarage speed an ion will be accelerated to is 30.000 m/s. This will result in a gain in velocity of the spacecraft , according to Newton's 3rd law. Calculate how many velocity a spacecraft with a mass of 1000 kg can gain by shooting away 50kg of Xenon 1+ iones.

Xenon 1+ iones will be shot from the back of the spacecraft with high speeds, the avarage speed an ion will be accelerated to is 30.000 m/s. This will result in a gain in velocity of the spacecraft , according to Newton's 3rd law. Calculate how many velocity a spacecraft with a mass of 1000 kg can gain by shooting away 50kg of Xenon 1+ iones.

My attempt:

Mass of one Xenon +1 ion:

= 131.30 x 1.660538921 x 10^-27 =

**2.18 x 10^-25 kg**

Kinetic energy gain of ion:

1/2 mv^2 = 1/2* 2.18*10^-25 *30000^2 =

**9.81*10^-17 Joule**

According to Newton's third law the gain in kinetic energy of the ion should be equal to the gain in kinetic energy of the spacecraft , right?

*(not sure about this)*1/2 mv^2 = 1/2 * 1000 * v^2 = 9.81*10^-17

**v = 4.43 * 10^-10 m/s for every ion shot**

Calculating how many iones we have:

100000 / 131.30u = 761.614 mol.

761.614 * 6,022 * 10^23 =

**4.586 * 10^26 iones.**

Shooting away all those iones will create a gain in speed of:

4.586 * 10^26 * 4.43 * 10^-10 =

**2.03 * 10^17 m/s**

**But since this is about a few thousand times the speed of light, I assume I did something wrong somewhere. If anyone could help me I'd be very thankful.**

Sander.