Final Velocity Question

sona1177

1. The problem statement, all variables and given/known data

A rock is tossed straight up with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep.

What is the rock's velocity as it hits the bottom of the hole?



2. Relevant equations
V = Vo + at
Y - Yo = Vot + .5at2
v2 = vo2 + 2a(Y - Yo)
Y - Yo = .5(Vo + V)t

3. The attempt at a solution
My answer is -24 m/s but the book reports positive 24 m/s. I don't see why this is the answer if the rock is moving downward. I've identified up as the positive direction. I got my answer by using equation v2 = vo2 + 2a(Y - Yo) where V was unknown, Vo =20 m/s, a=-9.8, displacement=-10. I know the calculator only gives positive square roots but you can have negative square roots also and since this object is moving down, shouldn't the velocity be -24 m/s. The question later asks for time and according to the book, the value is 4.5 seconds using equation Y - Yo = Vot + .5at2 but this only true if you plug is -24 m/s not simply positive 24 m/s. This is why I don't see why the answer book doesn't report -24 m/s as the final velocity before it hits the bottom of the whole. This is very frustrating.

ehild

You are right. If the initial velocity is positive, the final one is negative. 24 m/s is the final speed.

ehild