Physics, 03.03.2020 17:10 williamwu2750

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.2 m/s. The car is a distance d away. The bear is 29 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

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Answer from: maddihamidou

Explanation:

It is known that the relation between speed and distance is as follows.

velocity = $\frac{distance}{time}$

As it is given that velocity is 6 m/s and distance traveled by the bear is (d + 29). Therefore, time taken by the bear is calculated as follows.

$t_{bear} = \frac{(d + 29)}{6 m/s}$ ............. (1)

As the tourist is running in a car at a velocity of 4.2 m/s. Hence, time taken by the tourist is as follows.

$t_{tourist} = \frac{d}{4.2}$ ............. (2)

Now, equation both equations (1) and (2) equal to each other we will calculate the value of d as follows.

$t_{bear} = t_{tourist}$

$\frac{(d + 29)}{6 m/s}$ = $\frac{d}{4.2}$

4.2d + 121.8 = 6d

d = $\frac{121.8}{1.8}$

= 67.66

Thus, we can conclude that the maximum possible value for d is 67.66.

Answer from: Quest

scientific laws are the result of testing theories and proving them to be facts.

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4...