Thank you for visiting A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground The equation. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve the problem of finding out how long it takes for the basketball to go into the hoop at a height of 10 feet after being thrown, we need to use the given height equation:
[tex]\[ h = -16t^2 + 23t + 7 \][/tex]
This equation gives the height [tex]\( h \)[/tex] of the basketball [tex]\( t \)[/tex] seconds after it is thrown. We are looking for the time [tex]\( t \)[/tex] when the basketball's height is 10 feet, hence we set [tex]\( h \)[/tex] to 10 and solve the equation:
[tex]\[ -16t^2 + 23t + 7 = 10 \][/tex]
Rearrange the equation for a standard quadratic form:
[tex]\[ -16t^2 + 23t + 7 - 10 = 0 \][/tex]
Which simplifies to:
[tex]\[ -16t^2 + 23t - 3 = 0 \][/tex]
Now, we solve this quadratic equation using the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where [tex]\( a = -16 \)[/tex], [tex]\( b = 23 \)[/tex], and [tex]\( c = -3 \)[/tex].
First, we find the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 23^2 - 4 \times (-16) \times (-3) \][/tex]
Calculate the square of [tex]\( b \)[/tex]:
[tex]\[ 23^2 = 529 \][/tex]
Calculate [tex]\( 4ac \)[/tex]:
[tex]\[ 4 \times 16 \times 3 = 192 \][/tex]
Subtract:
[tex]\[ 529 - 192 = 337 \][/tex]
Now, with the discriminant calculated, we can find the roots using the quadratic formula:
Calculate the square root of the discriminant:
[tex]\[ \sqrt{337} \][/tex]
Then solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{-23 \pm \sqrt{337}}{-32} \][/tex]
There are two possible solutions for [tex]\( t \)[/tex], one positive and one negative. Since time cannot be negative, we only consider the positive solution:
The positive solution gives:
[tex]\[ t \approx 1.29 \text{ seconds} \][/tex]
Therefore, the basketball goes into the hoop approximately 1.29 seconds after it is thrown.
[tex]\[ h = -16t^2 + 23t + 7 \][/tex]
This equation gives the height [tex]\( h \)[/tex] of the basketball [tex]\( t \)[/tex] seconds after it is thrown. We are looking for the time [tex]\( t \)[/tex] when the basketball's height is 10 feet, hence we set [tex]\( h \)[/tex] to 10 and solve the equation:
[tex]\[ -16t^2 + 23t + 7 = 10 \][/tex]
Rearrange the equation for a standard quadratic form:
[tex]\[ -16t^2 + 23t + 7 - 10 = 0 \][/tex]
Which simplifies to:
[tex]\[ -16t^2 + 23t - 3 = 0 \][/tex]
Now, we solve this quadratic equation using the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where [tex]\( a = -16 \)[/tex], [tex]\( b = 23 \)[/tex], and [tex]\( c = -3 \)[/tex].
First, we find the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 23^2 - 4 \times (-16) \times (-3) \][/tex]
Calculate the square of [tex]\( b \)[/tex]:
[tex]\[ 23^2 = 529 \][/tex]
Calculate [tex]\( 4ac \)[/tex]:
[tex]\[ 4 \times 16 \times 3 = 192 \][/tex]
Subtract:
[tex]\[ 529 - 192 = 337 \][/tex]
Now, with the discriminant calculated, we can find the roots using the quadratic formula:
Calculate the square root of the discriminant:
[tex]\[ \sqrt{337} \][/tex]
Then solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{-23 \pm \sqrt{337}}{-32} \][/tex]
There are two possible solutions for [tex]\( t \)[/tex], one positive and one negative. Since time cannot be negative, we only consider the positive solution:
The positive solution gives:
[tex]\[ t \approx 1.29 \text{ seconds} \][/tex]
Therefore, the basketball goes into the hoop approximately 1.29 seconds after it is thrown.
Thank you for reading the article A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground The equation. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
