QuestionA golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the golf ball is130 feet per second. . The inclination of the hit is $45^{\circ}$ to the horizontal.
3. The height $h$ of the golf ball is given by the function $h(x)=\frac{-32 x^{}}{130^{}}+x$ where $x$ is the horizontal distance that the golf ball has traveled.

STEP 2

We are asked to find the value of $h(400)$ . This means we need to substitute $x=400$ into the function $h(x)$ .
$h(400)=\frac{-32 (400)^{2}}{130^{2}}+400$

STEP 3

First, calculate the value of $400^{2}$ .
$400^{2} =160000$ So, the equation becomes $h(400)=\frac{-32 \times160000}{130^{2}}+400$

STEP 4

Next, calculate the value of $130^{2}$ .
$130^{2} =16900$ So, the equation becomes $h(400)=\frac{-32 \times160000}{16900}+400$

STEP 5

Now, calculate the value of $-32 \times160000$ .
$-32 \times160000 = -5120000$ So, the equation becomes $h(400)=\frac{-5120000}{16900}+400$

STEP 6

Calculate the value of $\frac{-5120000}{16900}$ .
$\frac{-5120000}{16900} \approx -302.96$ So, the equation becomes $h(400)=-302.96+400$

STEP 7

Finally, calculate the value of $-302.96+400$ .
$-302.96+400 =97.04$ So, $h(400) =97.04$ feet.
This value represents the height of the golf ball when it has traveled a horizontal distance of400 feet.

Was this helpful?

QuestionA golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Round to two decimal places.

Studdy Solution

STEP 1

STEP 2

We are asked to find the value of $h(400)$ . This means we need to substitute $x=400$ into the function $h(x)$ .
$h(400)=\frac{-32 (400)^{2}}{130^{2}}+400$

STEP 3

First, calculate the value of $400^{2}$ .
$400^{2} =160000$ So, the equation becomes $h(400)=\frac{-32 \times160000}{130^{2}}+400$

STEP 4

Next, calculate the value of $130^{2}$ .
$130^{2} =16900$ So, the equation becomes $h(400)=\frac{-32 \times160000}{16900}+400$

STEP 5

Now, calculate the value of $-32 \times160000$ .
$-32 \times160000 = -5120000$ So, the equation becomes $h(400)=\frac{-5120000}{16900}+400$

STEP 6

Calculate the value of $\frac{-5120000}{16900}$ .
$\frac{-5120000}{16900} \approx -302.96$ So, the equation becomes $h(400)=-302.96+400$

STEP 7

Finally, calculate the value of $-302.96+400$ .
$-302.96+400 =97.04$ So, $h(400) =97.04$ feet.
This value represents the height of the golf ball when it has traveled a horizontal distance of400 feet.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA golf ball is hit at 130 ft/s at 45∘45^{\circ}45∘. Find h(400)h(400)h(400) using h(x)=−32x21302+xh(x)=\frac{-32 x^{2}}{130^{2}}+xh(x)=1302−32x2​+x. Round to two decimal places.

Studdy Solution

STEP 1

STEP 2

We are asked to find the value of h(400)h(400)h(400). This means we need to substitute x=400x=400x=400 into the function h(x)h(x)h(x).h(400)=−32(400)21302+400h(400)=\frac{-32 (400)^{2}}{130^{2}}+400h(400)=1302−32(400)2​+400

STEP 3

First, calculate the value of 4002400^{2}4002.4002=160000400^{2} =1600004002=160000So, the equation becomesh(400)=−32×1600001302+400h(400)=\frac{-32 \times160000}{130^{2}}+400h(400)=1302−32×160000​+400

STEP 4

Next, calculate the value of 1302130^{2}1302.1302=16900130^{2} =169001302=16900So, the equation becomesh(400)=−32×16000016900+400h(400)=\frac{-32 \times160000}{16900}+400h(400)=16900−32×160000​+400

STEP 5

Now, calculate the value of −32×160000-32 \times160000−32×160000.−32×160000=−5120000-32 \times160000 = -5120000−32×160000=−5120000So, the equation becomesh(400)=−512000016900+400h(400)=\frac{-5120000}{16900}+400h(400)=16900−5120000​+400

STEP 6

Calculate the value of −512000016900\frac{-5120000}{16900}16900−5120000​.−512000016900≈−302.96\frac{-5120000}{16900} \approx -302.9616900−5120000​≈−302.96So, the equation becomesh(400)=−302.96+400h(400)=-302.96+400h(400)=−302.96+400

STEP 7

Finally, calculate the value of −302.96+400-302.96+400−302.96+400.−302.96+400=97.04-302.96+400 =97.04−302.96+400=97.04So, h(400)=97.04h(400) =97.04h(400)=97.04 feet.This value represents the height of the golf ball when it has traveled a horizontal distance of400 feet.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Round to two decimal places.

We are asked to find the value of $h(400)$ . This means we need to substitute $x=400$ into the function $h(x)$ .
$h(400)=\frac{-32 (400)^{2}}{130^{2}}+400$

First, calculate the value of $400^{2}$ .
$400^{2} =160000$ So, the equation becomes $h(400)=\frac{-32 \times160000}{130^{2}}+400$

Next, calculate the value of $130^{2}$ .
$130^{2} =16900$ So, the equation becomes $h(400)=\frac{-32 \times160000}{16900}+400$

Now, calculate the value of $-32 \times160000$ .
$-32 \times160000 = -5120000$ So, the equation becomes $h(400)=\frac{-5120000}{16900}+400$

Calculate the value of $\frac{-5120000}{16900}$ .
$\frac{-5120000}{16900} \approx -302.96$ So, the equation becomes $h(400)=-302.96+400$

Finally, calculate the value of $-302.96+400$ .
$-302.96+400 =97.04$ So, $h(400) =97.04$ feet.
This value represents the height of the golf ball when it has traveled a horizontal distance of400 feet.