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Lera25 [3.4K]
3 years ago
5

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.9 m/s. The car is a distanc

e d away. The bear is 23 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
Physics
1 answer:
sammy [17]3 years ago
6 0
If it takes t seconds to reach the car, then the distance d is 3.9t.

The bear's distance from the tourist's starting point is
6t-23

For maximum d, we set the equations equal to each other:
3.9t=6t-23
\Rightarrow -2.1t=-23
\Rightarrow t=\frac{23}{2.1}
so the distance is
d=3.9(\frac{23}{2.1})\approx42.741\ m
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         w = \frac{2 \pi}{138240}

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At the point when the rocket is on a circular orbit  

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              \frac{GMm}{r^2} = mr w^2

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            M is the mass of the earth with a constant value of M = 5.98*10^{24}kg

            r is the distance between earth and circular orbit where the rocke is found

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                     r = \sqrt[3]{\frac{GM}{w^2} }

                        = \sqrt[3]{\frac{6.67*10^{-11} * 5.98*10^{24}}{(4.45*10^{-5})^2} }

                        = 5.78 *10^7 m

The orbital speed is represented mathematically as

                   v=wr

Substituting value

                  v= (5.78*10^7)(4.54*10^{-5})

                     v= 2.6*10^{3} m/s    

The escape velocity is mathematically represented as

                            v_e = \sqrt{\frac{2GM}{r} }

Substituting values

                             = \sqrt{\frac{2(6.67*10^{-11})(5.98*10^{24})}{5.78*10^7} }

                             v_e= 3.72 *10^3 m/s

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3 years ago
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