Answer:
Explanation:
Average velocity is change in position over the change in time. You have to take the directions into account. 100km east and then 100km south. That forms a right triangle, so you can use Pythagorean's theorem to find the hypotenuse which would be the displacement from his initial position:
[tex]\sqrt{100^2+100^2} = \sqrt{20,000}=141.42km[/tex]
Now take the displacement and divide it by the time it took to do the trip, 3 hours:
[tex]141.42km/3hours=47.14km/h[/tex]
The average velocity of the motion is 47.1 km/hr.
The given parameters;
The sketch of the motion can be demonstrated as follows;
100 km
P → → → → →
↓
↓ 100 km
↓ Q
The line joining P and Q is the resultant displacement = hypotenuse side of the right triangle.
The resultant displacement or total displacement is calculated as follows;
[tex]R^2 = 100^2 + 100^2\\\\R^2 = 20,000\\\\R = \sqrt{20,000} \\\\R = 141.4 \ km[/tex]
The average velocity is the total displacement per total time of the motion;
[tex]v = \frac{total \ displacement }{total \ time} \\\\v = \frac{R}{t_1+t_2} \\\\v = \frac{141.4}{1+3} \\\\v = 47.1 \ km/hr[/tex]
Thus, the average velocity of the motion is 47.1 km/hr.
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