Question

multiple choice 1 point
kelly the triathlete swims 1.5 km east, then bikes 40 km north, and then runs 10 km west. which choice gives the correct solution for the resultant? (clue: draw tip - to - tail vectors and see if you can use geometry to solve)
$r^{2}=40^{2}+8.5^{2}$
$r^{2}=10^{2}+40^{2}-2(1.5)(10)cos40$
$r^{2}=10^{2}-40^{2}$
$r^{2}=40^{2}+10^{2}-2(40)(1.5)cos10$
clear my selection

Explanation:

Step1: Analyze horizontal displacement

The athlete swims 1.5 km east and then runs 10 km west. The net horizontal displacement is $1.5 - 10=- 8.5$ km (negative indicates west - direction). The vertical displacement is 40 km north.

Step2: Apply Pythagorean theorem for resultant

The resultant displacement $R$ forms the hypotenuse of a right - triangle with horizontal and vertical sides. According to the Pythagorean theorem $R^{2}=a^{2}+b^{2}$, where $a = 40$ (vertical side) and $b = 8.5$ (horizontal side). So $R^{2}=40^{2}+8.5^{2}$.

Answer:

$R^{2}=40^{2}+8.5^{2}$ (the first option)