Question 82301
s(t)= -16t^2+64t+80
When it reaches the ground the height will be zero so
{{{0=-16t^2+64t+80}}}
Divide each side of the equation 16 to simplify the numbers involved.
{{{0=-t^2+4t+5}}}
Multiply both sides of the equation by -1 to eliminate the negative sign in front of the t squared.
{{{0=t^2-4t-5}}}
Factorise the trinomial.
{{{0=(t-5)(t+1)}}}
ie t=5 or t=-1.
The first answer shows the object hits the ground after 5 seconds and the second shows that it was at ground level 1 second before it was thrown upwards.
In the context of the problem the 5 second answer must be the solution.