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QuestionA golf ball is hit at 130 ft/s at 45∘45^{\circ}. Find h(400)h(400) 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 angle of inclination to the horizontal is 45∘45^{\circ}.
3. The height hh of the golf ball is given by the function h(x)=−32x130+xh(x)=\frac{-32 x^{}}{130^{}}+x.
4. xx is the horizontal distance that the golf ball has traveled.

STEP 2

We are asked to interpret the value of h(400)h(400). This means we need to substitute x=400x =400 into the function h(x)h(x) and calculate the result.
h(400)=−32⋅40021302+400h(400)=\frac{-32 \cdot400^{2}}{130^{2}}+400

STEP 3

First, calculate the square of400 and multiply it by -32.
−32⋅4002=−32⋅160000=−5120000-32 \cdot400^{2} = -32 \cdot160000 = -5120000

STEP 4

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

STEP 5

Now, divide the result from step3 by the result from step4.
−512000016900=−302.9585798816568\frac{-5120000}{16900} = -302.9585798816568

STEP 6

Finally, add400 to the result from step5.
−302.9585798816568+400=97.0414201183432-302.9585798816568 +400 =97.0414201183432So, h(400)=97.0414201183432h(400) =97.0414201183432.
The interpretation of this result is that when the golf ball has traveled400 feet horizontally, it is approximately97.04 feet above the ground.

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