Please help me explain this topic to my students.

This problem is on Slide 158, #51.


A dropped ball falls -8.0 meters.  What is its final speed?

Since the question asked for speed, it does not matter if the answer is a positive or a negative quantity.  However, the 3rd kinematic equation has velocity as part of the equation, and the answer should be in a negative quantity since the object reached the ground from falling.

The presenter explained that the answer cannot be in a positive quantity because the velocity is squared in the kinematic equation 3:  (V final)^2 = (V initial)^2 + 2a(X final - X initial)

The explanation makes sense.  However, can you please help me explain why the answer is in the positive quantity when it should be in a negative quantity? 

Thanks as always!

Joan, this is a case where the math gives two solutions, and you have to pick one based on the problem. The down direction is negative - as both a = -g and delta y = final minus initial = (0-8) = -8, so the square root works - you get the square root of a positive number.

BUT - the actual answer when you take a square root is plus or minus the square root. So, you get two solutions - 8 m/s and -8 m/s. Fortunately the question just asks for speed so it's 8 m/s. If it wanted a vector answer, you'd say -8 m/s or it's 8 m/s in the down direction.

John

Thank you so much!