Question

I inserted a picture of the question…this is a math/physics question

Answer 1

Given the equation:

`t=\sqrt[]{(8t+24)/(16)}`

WHere t is the time it takes for the music player to fall from the bridg to the bottom of the ravine.

Let's solve for t.

To solve for t, apply the following steps:

• Step 1.

Square both sides

`\begin{gathered} t^2=(\sqrt[]{(8t+24)/(16)})^2 \\ \\ t^2=(8t+24)/(16) \end{gathered}`

• Step 2.

Multiply both sides by 16:

`\begin{gathered} 16t^2=(8t+24)/(16)*16 \\ \\ 16t^2=8t+24 \end{gathered}`

• Step 3.

Divide all terms by 8:

`\begin{gathered} (16t^2)/(8)=(8t)/(8)+(24)/(8) \\ \\ 2t^2=t+3 \end{gathered}`

• Step 4.

Equate to zero and factor the left side:

`\begin{gathered} 2t^2-t-3=0 \\ \\ (t+1)(2t-3)=0 \end{gathered}`

Equate the individual factors to zero and solve for t:

`\begin{gathered} t+1=0 \\ \text{Subtract 1 from both sides:} \\ t+1-1=0-1 \\ t=-1 \\ \\ \\ 2t-3=0 \\ \text{Add 3 to both sides:} \\ 2t-3+3=0+3 \\ 2t=3 \\ Divide\text{ both sides by 2:} \\ (2t)/(2)=(3)/(2) \\ t=1.5 \end{gathered}`

Therefore, the values of t are:

t = -1, 1.5

Let the time be the positive value.

t = 1.5 seconds

This means it will take the music player 1.5 seconds to reach the bottom of the rivine.

Since it will take 1.5 seconds to reach the bottom of the ravine and the ballon will release after 1 second, the safety ballon will release in time.

ANSWER:

• Yes, the safety ballon will release in time.

• It will take the music player 1.5 seconds to fall to the bottom of the ravine.

• t = -1

,

• t = 1.5