How to Determine the Vertical Distance Travelled by a Rocket

Trigonometry functions have plenty of everyday uses. You can use a trigonometry function to determine how far a projectile travels vertically over a certain period of time.

For example, say a rocket is shot off and travels vertically while a scientist, who’s a mile away, watches its flight. One second into the flight, the angle of elevation of the rocket is 30 degrees. Two seconds later, the angle of elevation is 60 degrees. How far did the rocket travel in those two seconds?

A rocket, one mile from a scientist, rises vertically.

The preceding figure shows the rocket rising vertically.

1. Identify the parts of the triangles that you can use to solve the problem.

   In the figure, you can see two right triangles. One is superimposed on the other and shares a side — the adjacent side. In both triangles, the relevant sides are those that are adjacent and opposite the angles of elevation.

2. Determine which trig function to use.

   The tangent function uses the adjacent and opposite sides.

3. Write equations with the trig functions.

   

4. Solve for the values of x and y.

   The tangents of 30-degree and 60-degree angles are convenient values:

   

   To solve for y, the distance traveled in the second two seconds, substitute the value for x in the second equation to get:

   

   The rocket rose about 1.155 miles in two seconds.