(Help) Surface charge density (σ) for particle to hit plate...

[chrisbroward]

Homework Statement

Find surface charge density required for t = 11.4 ms (11.4 * 10^-3 s)

Answer in μC/m^2

Relevant Equations

q = -3.84 mC (-3.84 * 10^-3 C)
m = 3.38 g
ⱴ = 6.81 km/s (6810 m/s)
θ = 69.1°
all at t = 0.

I don't know if i'm exactly right.

But I started with x(time) = V cos θ t
which = (6810 m/s) cos (69.1°) (11.4 * 10^-3 s)
is ... 27.69 m

& since Electric field due to uniformly charge surface is represented by...
E = (q * σ)/(2 * ε_0 * m), and since acceleration (a) can be expressed as F/m, and Force (F) can be express as q*E;
I can combine these two equations...

a must be = (-3.84 * 10^-3 * σ)/(2 * (8.85 * 10^-12) * (3.38 * 10^-3)),
which is -6.418 * 10^10 * σ = a.

But as you can see now I have two unknowns and can't solve :(

Can anyone outline what exactly i'm doing incorrectly?

 

[osilmag]

You would want to find acceleration another way. Since you know t/2 and can find the velocity in the y-direction, you can use kinematics to find the acceleration.

 

[Orodruin]

Apart from the above: Please use units.

 

[haruspex]

Are you used to using the SUVAT equations in ballistics questions?

 

[kuruman]

Or knowing $v_x$ and the time of flight you can find the range. What is an expression for the range for a projectile that returns to the same level from which it was launched?