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Though this equation is very straightforward and easy to remember, in order to get full credit for your answer in a free response question, you'll typically need to show a derivation for a formula not already on your equation sheet.

However, to understand this derivation, it is necessary you know the following kinematic equation (which is the second equation on your equation sheet) and how to use it:

The Derivation

  1. This derivation utilizes the equation above by applying the equation to vertical coordinates:

2. On a flat plane, the final height and initial height are the same value, thus cancelling on both sides of the equation:

3. This is now just an exercise in finding the zeros of a quadratic. The next step is to factor the equation out:

4. There are now two solutions to this equation:

5. For this specific purpose, we ignore the zero solution because we're only interested in the time the projectile takes to complete its flight, which is clearly non-zero. Solving for time and using the formula for the vertical component of velocity:

Example

1. A cannon fires a cannonball across a field at an initial speed of 19.6 m/s, and it lands 2.00 seconds after being fired. What angle is the cannonball propped up to with respect to the field?

Your givens are:

Using the derivation above to solve for the angle:

Multiple Choice vs. Free Response

Although, in the example above I went straight for the flight time formula, it's important that you show ALL your work for free response questions, including the derivation of the formula using formulas given to you on your equation sheet.

However, on a multiple choice question, do NOT waste your time going through the derivation. 

One of the most significant killers for students' scores isn't not knowing the physics, but rather not having enough time.

Utilize your time as efficiently as possible, which includes skipping derivations when you have the opportunity to.

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