Answer:
a) The building is 150 m tall
b) h(t)=-5(t+6)(t-5)
c) The stone hits the ground at 5 seconds.
Step-by-step explanation:
Function Models
The path of a stone thrown down from a tall building is modeled by the function:
[tex]h(t)=150-5t-5t^2[/tex]
Where h is the height in meters and t is the time in seconds after the stone is thrown.
a) To find the height of the building, we set t=0 because it's the moment when the stone is thrown and has the same height as the building:
[tex]h(0)=150-5*0-5*0^2[/tex]
[tex]h(0)=150[/tex]
The building is 150 m tall
b) The function is
[tex]h(t)=150-5t-5t^2[/tex]
Factoring out -5:
[tex]h(t)=-5(-30+t+t^2)[/tex]
Rearranging:
[tex]h(t)=-5(t^2+t-30)[/tex]
To factor the polynomial in parentheses, we must find two numbers whose product is -30 and sum is 1. We can also use the quadratic formula to find the roots and factor later.
These numbers are 6 and -5, thus the function is:
[tex]h(t)=-5(t+6)(t-5)[/tex]
c) The stone hits the ground when h=0:
[tex]-5(t+6)(t-5)=0[/tex]
The equation has two solutions:
t = -6
t = 5
The only feasible solution is t = 5, thus the stone hits the ground at 5 seconds.
