Which equation and solution tells how long it takes the object to reach a height of 84 feet if its initial height is 180 feet?
180 = 84 – 16t²
t = -√6
84 = 180 – 16t²
t = √6
180 = 84 – 16t²
t = -√7
84 = 180 – 16t²
t = √7
Which equation and solution tells how long it takes the object to reach a height of 84 feet if its initial height is 180 feet?
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To find out how long it takes for the object to reach a height of 84 feet from an initial height of 180 feet, we can use the equation that describes the height of an object in free fall:
[ h = h_0 – 16t^2 ]
where ( h ) is the height at time ( t ), ( h_0 ) is the initial height, and ( -16t^2 ) is the term for the height decreasing due to gravity (in feet).
We set up the equation:
[ 84 = 180 – 16t^2 ]
Now, we solve for ( t ):
1. Subtract 180 from both sides:
[ 84 – 180 = -16t^2 ]
[ -96 = -16t^2 ]
2. Divide by -16:
[ t^2 = frac{96}{16} ]
[ t^2 = 6 ]
3. Take the square root of both sides:
[ t = sqrt{6} ]
Since time cannot be negative, we discard the negative solution. Thus, the correct equation and solution is:
Answer:
84 = 180 – 16t²
t = √6
This means it takes ( sqrt{6} ) seconds for the object to reach a height of 84 feet. For more in-depth assistance,
To determine how long it takes for an object to reach a height of 84 feet starting from an initial height of 180 feet, we can use the equation:
[ h(t) = 180 – 16t^2 ]
where ( h(t) ) is the height in feet at time ( t ) in seconds.
We set the height equal to 84 feet:
[ 84 = 180 – 16t^2 ]
Now, we can solve for ( t ):
1. Subtract 180 from both sides:
[ 84 – 180 = -16t^2 ]
[ -96 = -16t^2 ]
2. Divide both sides by -16:
[ t^2 = frac{96}{16} ]
[ t^2 = 6 ]
3. Take the square root of both sides:
[ t = sqrt{6} ]
Since time cannot be negative, we discard the negative root.
So, the correct option is:
84 = 180 – 16t²
t = √6
This indicates that it takes (sqrt{6}) seconds for the object to reach a height of 84 feet. If you’d like more detailed assistance, feel free to check the extended services page!
The correct equation is:
84 = 180 – 16t²
t = √6
### Explanation:
This equation models the height of the object over time, where 180 is the initial height, and 16t² represents the effect of gravity on the height. We set the height equal to 84 feet to find the time (t). When you solve for t, you find that t = √6, which tells you how long it takes for the object to reach a height of 84 feet. Keep practicing, and check out our extended services page if you need more help!
To find out how long it takes for the object to reach a height of 84 feet when it starts at 180 feet, we’ll use the equation:
[ 84 = 180 – 16t^2 ]
This equation represents the height of the object over time, where 16 is the acceleration due to gravity in feet per second squared (assuming the object is thrown upward).
Now, let’s solve the equation:
1. Rearrange the equation to isolate ( t^2 ):
[ 16t^2 = 180 – 84 ]
[ 16t^2 = 96 ]
2. Divide both sides by 16:
[ t^2 = frac{96}{16} ]
[ t^2 = 6 ]
3. Take the square root of both sides to find ( t ):
[ t = sqrt{6} ]
Therefore, the correct answer is:
[ t = sqrt{6} ]
This indicates it takes ( sqrt{6} ) seconds for the object to reach a height of 84 feet.
Great job working through this! If you have any more questions or need further help, feel free to ask!