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QuestionFind how many times greater the max speed of a giraffe (L=6L=6 ft) is than a hippo (L=3L=3 ft) using S=gLS=\sqrt{g L} with g=32g=32.

Studdy Solution

STEP 1

Assumptions1. The maximum walking speed $$ of an animal is given by the equation $=\sqrt{g L}$. . The constant $g$ is given as $32 \, \text{ft/sec}^$.
3. The leg length of the giraffe is6 feet.
4. The leg length of the hippopotamus is3 feet.

STEP 2

First, we need to calculate the maximum walking speed of the giraffe. We can do this by substituting the values of gg and $$ into the equation.
giraffe=gLgiraffe_{giraffe} = \sqrt{g L_{giraffe}}

STEP 3

Now, plug in the given values for gg and giraffe_{giraffe} to calculate the maximum walking speed of the giraffe.
giraffe=32 ft/sec2×6 ft_{giraffe} = \sqrt{32 \, \text{ft/sec}^2 \times6 \, \text{ft}}

STEP 4

Calculate the maximum walking speed of the giraffe.
giraffe=192 ft2/sec2=13.86 ft/sec_{giraffe} = \sqrt{192 \, \text{ft}^2/\text{sec}^2} =13.86 \, \text{ft/sec}

STEP 5

Next, we need to calculate the maximum walking speed of the hippopotamus. We can do this by substituting the values of gg and $$ into the equation.
hippo=gLhippo_{hippo} = \sqrt{g L_{hippo}}

STEP 6

Now, plug in the given values for gg and hippo_{hippo} to calculate the maximum walking speed of the hippopotamus.
hippo=32 ft/sec2×3 ft_{hippo} = \sqrt{32 \, \text{ft/sec}^2 \times3 \, \text{ft}}

STEP 7

Calculate the maximum walking speed of the hippopotamus.
hippo=96 ft2/sec2=9.80 ft/sec_{hippo} = \sqrt{96 \, \text{ft}^2/\text{sec}^2} =9.80 \, \text{ft/sec}

STEP 8

Now that we have the maximum walking speeds of both the giraffe and the hippopotamus, we can find how many times greater the maximum walking speed of the giraffe is than that of the hippopotamus. We can do this by dividing the maximum walking speed of the giraffe by the maximum walking speed of the hippopotamus.
Times greater=giraffehippo\text{Times greater} = \frac{_{giraffe}}{_{hippo}}

STEP 9

Plug in the values for giraffe_{giraffe} and hippo_{hippo} to calculate how many times greater the maximum walking speed of the giraffe is than that of the hippopotamus.
Times greater=13.86 ft/sec9.80 ft/sec\text{Times greater} = \frac{13.86 \, \text{ft/sec}}{9.80 \, \text{ft/sec}}

STEP 10

Calculate how many times greater the maximum walking speed of the giraffe is than that of the hippopotamus.
Times greater=13.86 ft/sec9.80 ft/sec=.41 times\text{Times greater} = \frac{13.86 \, \text{ft/sec}}{9.80 \, \text{ft/sec}} =.41 \, \text{times}So, the maximum walking speed of a giraffe with a leg length of6 feet is.41 times greater than a hippopotamus with a leg length of3 feet.

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