Sue and Jenny kick a soccer ball at exactly
the same time. Sue’s foot exerts a force of
52.7 N to the north. Jenny’s foot exerts a
force of 91 N to the east.
a) What is the magnitude of the resultant
force on the ball?
Answer in units of N. b) What is the direction of the resultant force
(measured from East)?
Answer in units of ◦
.

a)

Answer:

Using Pythagorean Theorem.

[tex]F_{R} = \sqrt{Fn^{2} + Fe^{2} } \\\\ F_{R} = \sqrt{52.7^{2} + 91^{2} }\\\\ F_{R} = 105.16N[/tex]

b)

Answer:

[tex]tan^{-1} \frac{opp}{adj} \\ \\ tan^{-1} \frac{52.7}{91} \\ \\ = 30.08^{o}[/tex]

The resultant force of the two forces which are acting perpendicular to each other is 105.15 N and the direction is 59.91 ° from east.

Force is an external agent acting on a body to change it from the state of motion or rest. If two forces acting on a body and both are applied in the same direction, the resultant force will be the sum of two forces in magnitude.

If the two forces are in opposite directions, then the resultant force will be the substracted value of their magnitude. If one force is to the north and other is to the east, then they are perpendicular to each other.

Hence, to find the resultant force we can use the Pythagoras theorem for right angled triangle. The hypotenuse will be the resultant force.

Resultant force = √ (52.7² + 91² )

                          = 105. 15 N.

The direction of the force = Tan ⁻¹ (91 / 52.7 )

                                           = 59.91 ° from east to north.

Hence, the resultant force is 105.15 N with a direction of 59.91 ° from east.

To find more on resultant force, refer here:

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