Question

Maria drops a hammer from an apartment that is 30 meters above the ground. The height of the hammer in meters h, after t seconds is modeled by the function “ h(t)= -t2-2t+30. Find the approximate number of seconds it will take for the hammer to hit the ground

Answer 1

$h(t)=-t^2-2t+30;$

$D=b^2-4ac;$

$D=(-2)^2-(4×(-1)×30); D=4+120; D=124; \\ t_1=\frac{-b+\sqrt{D}}{2a};\sqrt{D}=11.14$

$t_2=\frac{-b-\sqrt{D}}{2a};$

$t_1=\frac{2+11.14}{-2}; t_2=\frac{2-11.14}{-2};$

$t_1=13.14/(-2)=-6.57;\\ t_2=-9.14/(-2)=4.57;$

time cannot be negative so the answer is 4.57 seconds.