Protons are projected with an initial speed v_0 = 9 550 m/s into a region where a uniform electric field E = 720 N/C is present (see figure). The protons are to hit a target that lies a horizontal distance of 1.27 mm from the point where the protons are launched. Find (a) the two projection angles theta that will result in a hit and (b) the total duration of flight for each of the two trajectories.

It is time to do physics. This particular problem is usually studied during the revision of concepts in electrical forces and electric fields. The trick is that the only electricity knowledge we will use is like getting the vertical acceleration. Let's do it

As we can see in the figure above, we only equated the electric force with the Newton's second law and then solve for the y-acceleration.

From here the problem transform into a projectile motion without surprise.

The unique "surprise" is that to can solve it we need use an especial equation called The Equation Ballistics (One of my favorite physics equations ).

We use trigonometric properties to convert the Equation Ballistics in a quadratic equation.

As we well know quadratic equations have two roots, that is to say two possible solutions to the equation, of those roots for tan (theta) we can clear the two possible angles hitting the target.

Then to get the flight time, we will use the maximum range equation.

That's all for this post. A little advice we can give you: Every time that problem ask you for 2 possible shooting angles, you must use Equation Ballistics .

If you like our work share it with your friends! see you later! and remember ... physics it's easy! very easy... ;)