in the review hw)
A football is kicked straight up from a height of 4 feet with an initial speed of 65 feet per second. The formula
after it was kicked. How long will it take for the football to hit the ground?
seconds (Use a calculator and round to the nearest tenth of a second.)

Ask by Maxwell Stuart. in the United States

Nov 07,2024

Question

in the review hw)
A football is kicked straight up from a height of 4 feet with an initial speed of 65 feet per second. The formula
after it was kicked. How long will it take for the football to hit the ground?
seconds (Use a calculator and round to the nearest tenth of a second.)

Ask by Maxwell Stuart. in the United States

Nov 07,2024

UpStudy AI · Accepted Answer

Given:
- Initial height, $$ h_0 = 4 $$ feet
- Initial speed, $$ v_0 = 65 $$ feet per second
- The formula for the height of the football after it was kicked is $$ h = -16t^2 + 65t + 4 $$

To find the time it takes for the football to hit the ground, we need to find the value of $$ t $$ when the height $$ h $$ is 0.

So, we set $$ h = 0 $$ in the formula and solve for $$ t $$:

$$ 0 = -16t^2 + 65t + 4 $$

Now, we can solve this quadratic equation to find the value of $$ t $$. Let's use the quadratic formula to solve for $$ t $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$-16t^{2}+65t+4=0$$
- step1: Multiply both sides:
  $$16t^{2}-65t-4=0$$
- step2: Solve using the quadratic formula:
  $$t=\frac{65\pm \sqrt{\left(-65\right)^{2}-4\times 16\left(-4\right)}}{2\times 16}$$
- step3: Simplify the expression:
  $$t=\frac{65\pm \sqrt{\left(-65\right)^{2}-4\times 16\left(-4\right)}}{32}$$
- step4: Simplify the expression:
  $$t=\frac{65\pm \sqrt{4481}}{32}$$
- step5: Separate into possible cases:
  $$\begin{align}&t=\frac{65+\sqrt{4481}}{32}\&t=\frac{65-\sqrt{4481}}{32}\end{align}$$
- step6: Rewrite:
  $$t_{1}=\frac{65-\sqrt{4481}}{32},t_{2}=\frac{65+\sqrt{4481}}{32}$$
The solutions to the quadratic equation are:
- $$ t_1 = \frac{65 - \sqrt{4481}}{32} $$
- $$ t_2 = \frac{65 + \sqrt{4481}}{32} $$

Since time cannot be negative, we will consider the positive solution. Let's calculate the approximate value of $$ t $$ by substituting the values into the expression.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(65+\sqrt{4481}\right)}{32}$$
- step1: Remove the parentheses:
  $$\frac{65+\sqrt{4481}}{32}$$
The approximate time it takes for the football to hit the ground is $$ t \approx 4.1 $$ seconds when rounded to the nearest tenth of a second.
The time it takes for the football to hit the ground is approximately 4.1 seconds.

in the review hw)
A football is kicked straight up from a height of 4 feet with an initial speed of 65 feet per second. The formula
after it was kicked. How long will it take for the football to hit the ground?
seconds (Use a calculator and round to the nearest tenth of a second.)

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in the review hw) A football is kicked straight up from a height of 4 feet with an initial speed of 65 feet per second. The formula after it was kicked. How long will it take for the football to hit the ground? seconds (Use a calculator and round to the nearest tenth of a second.)

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in the review hw)
A football is kicked straight up from a height of 4 feet with an initial speed of 65 feet per second. The formula
after it was kicked. How long will it take for the football to hit the ground?
seconds (Use a calculator and round to the nearest tenth of a second.)