Physics, 03.11.2019 21:31 kaadenday3629

Two rock climbers, bill and karen, use safety ropes of similar length. karen's rope is more elastic, called a dynamic rope by climbers. bill has a static rope, not recommended for safety purposes in pro climbing. karen falls freely about 2.0 m and then the rope stops her over a distance of 0.9 m.

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Answer from: tinyturtles

You never gave us an answer, so therefore, we can't answer this question.

Answer from: spdesch2558

The answer is 2.8 times.

Explanation:

Speed needs to be calculated when Karen completes the 2.0m drop, using the following equation:

V^2 = Vo^2 + 2gd = 0^2 + 2*9.81 m/s^2 * 2.0 m = 39.24 m^2/s^2 => V = 6.26 m/s

From there, the rope has a net force which causes a constant acceleration, which can be calculated according to the equation:

Vo = 6.26 m/s

Vf = 0

Vf^2 = Vo^2 + 2ad => a = [Vf^2 - Vo^2]/2d = [0^2 - (6.26 m/s)^2]/2*(0.9m) = -17.63 m/s^2

That acceleration is due to the difference between the force exerted by the rope and Karen's weight:

Karen's weight = mg

Karen's Weight - String Force = Net Force = ma

mg - chord force = ma

String strength = mg - ma = m (g -a) = m [9.81 m/s^2 - (-17.63m/s^2)] = 27.44m

Dividing by weight:

27.44m/9.81m = 2.79 = 2.8 times

The answer is three times.

Answer from: Quest

we have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is $[2,\infty)$ .

if we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

let us know find its inverse.

$y=(x-5)^{2}+2$

upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

let us now solve this function for y.

$(y-5)^{2}=x-2\\ y-5=\pm \sqrt{x-2}\\ y=5\pm \sqrt{x-2}\\$

hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

Answer from: Quest

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

$v_j = v_1 + v_2 = 3.100 + 1.350 = 4.45 m/s$

now the speed of paul will be same as it is given as he is running on the ground

$v_p = 3.100 m/s$

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

$\delta t = \frac{d}{v_j} - \frac{d}{v_p}$

$\delta t = \frac{2080}{4.450} - \frac{2080}{3.100}$

$\delta t = -203.55 s$

so jerome will reach first and the time difference will be 203.55 s or 3.4 min

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