Answer:
The hammer will hit the ground after 5 seconds.
Step-by-step explanation:
The height of hammer is defined by the function
[tex]h(t)=-t^2-t+30[/tex]
Where, t is time in seconds.
[tex]h(t)=-t^2-6t+5t+30[/tex]
[tex]h(t)=-t(t+6)+5(t+6)[/tex]
[tex]h(t)=(t+6)(5-t)[/tex]
The value of h(t) is 0, when hammer will hit the ground.
[tex]0=(t+6)(5-t)[/tex]
Equate each factor equal to 0.
[tex]t=-6[/tex]
[tex]t=5[/tex]
The time can not be negative, therefore hammer will hit the ground after 5 seconds.
