# Two-dimensional motion problem

1. Jun 23, 2007

### spizma

1. The problem statement, all variables and given/known data
It is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope can view such objects using an electron beam instead of a light beam. Electron microscopy has proved invaluable for investigations of viruses, cell membranes and subcellular
structures, bacterial surfaces, visual receptors, chloroplasts, and the contractile properties of muscles. The “lenses” of an electron microscope consist of electric and magnetic fields that control the electron beam. As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x axis in the xy plane with initial velocity $$\mathbf{v_i} = v_i \hat{i}$$ . As it passes through the region $$x = 0$$ to $$x = d$$, the electron experiences acceleration $$\mathbf{a} = a_x \hat{i} + a_y \hat{j}$$,where $$a_x$$ and $$a_y$$ are constants. For the case $$v_i = 1.80 \times 10000000$$ m/s, $$a_x = 8.00 \times 100000000000000$$ m/s^2 and $$a_y = 1.60 \times 1015$$ m/s^2, determine
at $$x = d = 0.0100$$ m the position of the electron

2. Relevant equations
$$x_f = x_i + v_xi t + .5 a_x t^2$$

3. The attempt at a solution
I can't seem to find the value of t. I've tried reorganizing equations I know that have t in them, but I can't get a value that, when plugged into the position as a function of time equation, makes sense. What am I missing?

Last edited: Jun 23, 2007
2. Jun 23, 2007

### malawi_glenn

$$x_f = x_i + v_xi t + .5 a_x t^2$$

What is the "i" after $$v_x$$
? Should it be: $$v_{xi}$$ as meant to be initial velocity in x-direction?

If you write more on how you tried to solve for t, we can help you more.

But are you sure how to solve a quadratic equation? Is that your problem?

$$at^{2} + bt + c = 0 ; t = - \frac{b}{a2} \pm \sqrt{(\frac{b}{a2})^{2} - c/2}$$

3. Jun 23, 2007

### spizma

I figured it out

Never mind! I figured out the answer. To answer the above question, i just made a mistake in my latex code; the i should be subscripted as it represents initial. If your interested in how I found the answer, I found the velocity of the electron at d using the equation $$v^2_{xf} = v^2_{xi} + 2 a_x (x_f - x_i)$$ and then plugging that value into the equation $$v_{xf} = v_{xi} + a_x t$$ and solving for t. From there the problem is very easy.

Last edited: Jun 23, 2007