# Calculus

Emily and Clare kick a soccer ball at the same time. Emily kicks it with a force of 120 N at an angle of 60 degrees and Clare kicks it with a force of 200 N at an angle of 120 degrees. The angles are measured from a line between the centres of the two goals.

Calculate the magnitude and direction of the resultant force.

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1. The problem can be solved by resolving each applied force into its components. Sum the components individually to get the components of the resultant force.

Let
f1=120N, θ1=60°
f2=200N, θ2=120°

Fx=f1.cos(θ1)+f2.cos(θ2)
Fy=f1.sin(θ1)+f2.sin(θ2)

Magnitude of resultant force
= sqrt(Fx²+Fy²)
Angle of resultant force
= tan-1(Fy/Fx)

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2. 280N

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3. 280N

98.2°

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