Question

if a rock falls from a height of 20 meters on the earth. the height h in meters after t seconds is given by h (t)=-4.9t^2+20. ...find h (2) and explain....find h (t)=0

Answer 1

First, we'll find h(2):

$h(t)=-4.9t^2+20\\\\ h(2)=-4.9\cdot2^2+20\\\\ h(2)=-4.9\cdot4+20\\\\ h(2)=-19.6+20\\\\ \boxed{h(2)=0.4~m}$

Now, we'll find when h(t)=0:

$h(t)=0\\\\ -4.9t^2+20=0\\\\ 4.9t^2=20\\\\ t^2=\dfrac{20}{4.9}\\\\ t^2\approx4.08\\\\ t\approx\pm\sqrt{4.08}\\\\ \to\text{Since t represents the elapsed time, it is always positive:}\\\\ t\approx\sqrt{4.08}\\\\ \boxed{t\approx2.02~s}$