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A hiker walks 2.00 $\mathrm{km}$ north and then 3.00 $\mathrm{km}$ east, all in 2.50 hours. Calculate the magnitude and direction of the hiker's (a) displacement (in $\mathrm{km} )$ and (b) average velocity (in $\mathrm{km} / \mathrm{h}$ ) during those 2.50 hours. (c) What was her average speed during the same time interval?

(a) $\overrightarrow { \mathrm { d } } = 6.53 \mathrm { km }$ North-East

(b) $\vec { v } = 2.61 \mathrm { km } \mathrm { h } ^ { - 1 }$ North-East

(c) $v = 2 \mathrm { km } \mathrm { h } ^ { - 1 }$

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Bobby N.

February 4, 2021

A solid metal ball is thrown directly downward, with an initial speed of 8.45m/s, from the top of a structure at a height of 3.9m. How much time (in s) does it take before striking the ground?

Cornell University

Rutgers, The State University of New Jersey

Numerade Educator

University of Sheffield

so we can say that for part A, the magnitude of the displacement is gonna be equal. In the square root of 2.0 kilometers quantity squared plus 3.0 kilometers squared. This would be equaling 3.6. You could say 3.61 kilometers. This would be the magnitude of our displacement. Four part a. Now four part. Uh, we want to say that we also want to find the direction for the for the displacement, rather so we can say that fate as equaling are tan. And we're travelling, uh, two kilometers north three kilometers east. So this should be the Ark 10 of 2.0 kilometers, divided by 3.0 kilometers two kilometers north three kilometers east. That puts us in the first quarter it so this is actually gonna be 33.7 degrees above the positive X axis. So this would be our answer for part a four part B. Then we want to find the average velocity. The average velocity is actually gonna be equaling the magnitude the displacement divided by time. And so this would be 3.61 or rather Let's round at the very end. So 3.6055 kilometers divided by 2.50 hours. This is giving us 1.44 kilometers per hour. And again it's the same exact direction, 33.7 degrees above the positive max access, or 33.7 degrees north of east. And then finally, for part C, we could say that what is her average speed world? Her average speed is actually going to be. There's no direction. So her average speed is simply going to be equally the total distance traveled, which in this case is 2.0 kilometers plus 3.0 kilometers. And then this would be divided bye again, 2.50 hours. And so this advert speed which actually takes into account the path traveled, is equaling two kilometers per hour. This would be our average speed. That is the end of the solution. Thank you for watching