Question

(PLSS HELPP!!) A barge is being towed by two tugboats, using ropes with force vectors as shown.

Answer 1

The angle between the ropes is 58 degree , Option C is the right answer.

What is a Vector ?

Vector is an object that has both magnitude and direction.

It is given in the question that

$\rm F_1 = 10000i +6000j\\F_2 = 13500 i -7000j$

The angle between the ropes can be calculated as

$\overrightarrow F_1 * \overrightarrow F_2 = |F_1| *|F_2| cos \theta$

$\rm F_1 = \sqrt{10000^2 + 6000^2}\\\\F_2 = \sqrt{ 13500^2 + 7000^2}$

$\rm F_1$ = 11662

$\rm F_2$ = 15207

$\overrightarrow F_1 * \overrightarrow F_2 = (11662 * 15207)\; cos \theta$

$\overrightarrow F_1 * \overrightarrow F_2$ = 93000000

93000000 = 11662 * 15207 cos $\rm \theta$

cos $\rm \theta$ =0.524

$\rm \theta$ = 58.37 degree

The angle between the ropes is 58 degree , Option C is the right answer.

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