An electron passes location
<0.02m, 0.04m,−0.06m>, and 4 μs later is de-
tected at location <0.02 m, 1.84 m,−0.86 m>.
Find the average velocity of the elecron:
¯v = <vx, vy, vz>
If the electron continues to travel at this av-
erage velocity, find where it will be in another
9 μs :
~d = <dx, dy, dz>
Answer in units of m
I've tried this question several times and I cannot get the second part correct.
For the first part I get <0, 450000, -200000>
But then for the second part I keep getting it wrong. for dx i get 0 which is correct, but for dy= .04+(5 * 450000) it says it's wrong. not sure what im doing wrong!
To find the average velocity of the electron, you need to calculate the change in position (∆r) and divide it by the change in time (∆t).
First, let's calculate the change in position (∆r) by subtracting the initial position from the final position:
∆r = <0.02 m, 1.84 m, −0.86 m> − <0.02 m, 0.04 m, −0.06 m>
= <0.02 m − 0.02 m, 1.84 m − 0.04 m, −0.86 m − (−0.06 m)>
= <0 m, 1.8 m, −0.8 m>
Next, we need to calculate the change in time (∆t), which is given as 4 μs.
Now, divide the change in position (∆r) by the change in time (∆t) to find the average velocity (∆v):
¯v = ∆r/∆t
= <0 m, 1.8 m, −0.8 m> / (4 * 10^-6 s)
= <0 m/s, 450000 m/s, -200000 m/s>
So, the average velocity of the electron is ¯v = <0 m/s, 450000 m/s, -200000 m/s>.
Now, let's find where the electron will be in another 9 μs.
Using the average velocity (∆v) we just calculated, we can find the change in position (∆r) by multiplying the average velocity by the change in time (∆t):
∆r = ¯v * ∆t
= <0 m/s, 450000 m/s, -200000 m/s> * (9 * 10^-6 s)
= <0 m/s, 4050 m, -1800 m>
Finally, to find the final position, which is the sum of the initial position and the change in position, we add the change in position (∆r) to the initial position:
~d = <0.02 m, 0.04 m, −0.06 m> + <0 m/s, 4050 m, -1800 m>
= <0.02 m + 0 m, 0.04 m + 4050 m, −0.06 m − 1800 m>
= <0.02 m, 4050.04 m, −1800.06 m>
Therefore, the electron will be at the position ~d = <0.02 m, 4050.04 m, -1800.06 m> after another 9 μs.
Please make sure to double-check your calculations and units to avoid any errors.