Answer to Question #147776 in Physics for Isabelle Gireada

Question

could you explain how you got t1= 2s and t2= 6s?

Answer 1

 Different answers in physics are usually a result of quadratic equations. For example, if you throw a body at 30 m/s vertically upward, and ask yourself "What time will it take to reach 2 meters above the ground?", the solution will be like this:

$$h=v_0t-\frac{gt^2}{2},\\\space\\ \frac{gt^2}{2}-v_0t+h=0.$$

We transformed a physical equation into a mathematical equation with greater powers of t on the left. Substitute values:

$$5t^2-30t+2=0.$$

This is a quadratic equation Replace numbers like this:

$$5=a, \\b=-30,\\c=2.$$

The solution for t is

$$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$

With numbers plugged in, it is

$$t=\frac{-(-30)\pm\sqrt{(-30)^2-4\cdot5\cdot2}}{2\cdot5}=0.07\text{ s or 5.9 s}.$$