Question

An object is thrown downward with an initial velocity of 8 feet per second. The relationship between the distance s it travels and time t is given by s = 8t + 16t². How long does it take the object to fall 80 feet?It takes___ seconds for the object to fall 80 feet.

Answer 1

We have the distance s in function of time expressed as:

`s=8t+16t^2`

We then have to find t so that s = 80 feet.

We can then find it as:

`\begin{gathered} s=80 \\ 8t+16t^2=80 \\ 8(t+2t^2)=80 \\ t+2t^2=(80)/(8) \\ 2t^2+t=10 \\ 2t^2+t-10=0 \end{gathered}`

We can calculate the solutions for this equation as:

`\begin{gathered} t=(-1\pm√(1^2-4(2)(-10)))/(2(2)) \\ t=(-1\pm√(1+80))/(4) \\ t=(-1\pm√(81))/(4) \\ t=(-1\pm9)/(4) \\ \Rightarrow t_1=(-1-9)/(4)=-(10)/(4)=-2.5 \\ \Rightarrow t_2=(-1+9)/(4)=(8)/(4)=2 \end{gathered}`

As time t has to be positive, the only valid solution in the context of this problem is t = 2 seconds.

Answer: It takes 2 seconds for the object to fall 80 feet.