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QuestionA golf ball is hit at 130 ft/s at 45∘45^{\circ}. Find height h(100)h(100) using h(x)=−32x21302+xh(x)=\frac{-32 x^{2}}{130^{2}}+x.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the golf ball is130 feet per second. . The golf ball is hit at an angle of 45∘45^{\circ} to the horizontal.
3. The height hh of the golf ball is given by the function h(x)=−32x130+xh(x)=\frac{-32 x^{}}{130^{}}+x where xx is the horizontal distance that the golf ball has traveled.

STEP 2

To find the height of the golf ball after it has traveled100 feet, we need to substitute x=100x =100 into the given function.
h(100)=−32×10021302+100h(100)=\frac{-32 \times100^{2}}{130^{2}}+100

STEP 3

First, calculate the square of100.
1002=10000100^{2} =10000

STEP 4

Substitute 1002100^{2} into the equation.
h(100)=−32×100001302+100h(100)=\frac{-32 \times10000}{130^{2}}+100

STEP 5

Calculate the product of -32 and10000.
−32×10000=−320000-32 \times10000 = -320000

STEP 6

Substitute −32×10000-32 \times10000 into the equation.
h(100)=−3200001302+100h(100)=\frac{-320000}{130^{2}}+100

STEP 7

Next, calculate the square of130.
1302=16900130^{2} =16900

STEP 8

Substitute 1302130^{2} into the equation.
h(100)=−32000016900+100h(100)=\frac{-320000}{16900}+100

STEP 9

Calculate the division of -320000 by16900.
−32000016900≈−18.93\frac{-320000}{16900} \approx -18.93

STEP 10

Substitute −32000016900\frac{-320000}{16900} into the equation.
h(100)=−18.93+100h(100)=-18.93+100

STEP 11

Calculate the sum of -18.93 and100.
−18.93+100=81.07-18.93+100 =81.07The height of the golf ball after it has traveled100 feet is approximately81.07 feet.

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