Finding Horizontal Speed of Electron in Electric Field

[Amahia11]

Homework Statement

So if an electron enters an electric field (between two charged parallel plates) at an angle (i.e not parallel to the x axis) and knowing that the speed is, say, 5 x 10^6 m/s, how would you find the HORIZONTAL velocity of the electron?

you know that horizontaly it must be (5 x 10^6)cos(theta) and that vertically it must therefore be (5 x 10^6)sin(theta) but how would you find the horizontal velocity?

please help, very appreciated! :)

Homework Equations

The Attempt at a Solution

I thought it might help knowing that sin(theta)/cos(theta) = tan(theta) ?
But no idea how to find the horizontal speed...

 

[tiny-tim]

Hi Amahia11 !

(have a theta: θ and try using the X² icon just above the Reply box )

I don't understand … what are the unkowns, and what is given?

If 5 x 10⁶ and θ are both given, then it's just 5 x 10⁶ cosθ. ​

 

[Amahia11]

Hi Amahia11 !

(have a theta: θ and try using the X² icon just above the Reply box )

I don't understand … what are the unkowns, and what is given?

If 5 x 10⁶ and θ are both given, then it's just 5 x 10⁶ cosθ. ​

hi tiny-tim! thanks for the tips! :D

Ok, basically my physics exam on particle dynamics in electric fields is next week and my teacher told us to remember that sinθ/cosθ=tanθ (something which we btw never used in class)

now i understand (you're right) that the horizontal component will be 5 x 19⁶cosθ but my question is how could you use the equation "sinθ/cosθ=tanθ"? I'm just trying to figure out how that could be useful in anyway... any ideas?

(sorry my initial post was quite unclear and vague!)

 

[tiny-tim]

Hi Amahia11!

Ok, basically my physics exam on particle dynamics in electric fields is next week and my teacher told us to remember that sinθ/cosθ=tanθ (something which we btw never used in class)

…but my question is how could you use the equation "sinθ/cosθ=tanθ"? I'm just trying to figure out how that could be useful in anyway... any ideas?

ahhh …

yes, you will find tan = sin/cos useful, not when you're given the angle, but when you want to find it …

for example, if you know that the horizontal component of a force is 13, and the vertical component is 10, then the magnitude will be √(100 + 169), and the angle from the horizontal will have tan = 10/13

btw, you should at some stage be learning the basic trigonometric formulas:

cos = adj/hyp
sin = opp/hyp
tan = opp/adj
(that's adjacent, opposite, hypotneuse )​

 

[rwisz]

To find the horizontal velocity of the electron, you can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. In this case, the initial horizontal velocity is (5 x 10^6)cos(theta) and the acceleration is 0, since there is no force acting on the electron in the horizontal direction. Therefore, the horizontal velocity remains constant and is equal to (5 x 10^6)cos(theta).