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.

280N

98.2°

but show the answers and how u got them u idiots

Well, it seems like Emily and Clare are having a real kick-off! Let's see what happens when their forces combine.

To find the resultant force, we need to break down both forces into their x and y components. Let's start with Emily's kick.

Emily's force (F_emily) has a magnitude of 120 N at an angle of 60 degrees. To find the x component (F_emily_x), we can use the formula F_emily_x = F_emily * cos(angle).

F_emily_x = 120 N * cos(60 degrees) = 120 N * 0.5 = 60 N

And for the y component (F_emily_y), we can use the formula F_emily_y = F_emily * sin(angle).

F_emily_y = 120 N * sin(60 degrees) = 120 N * 0.866 = 103.92 N

Now, let's do the same for Clare's kick.

Clare's force (F_clare) has a magnitude of 200 N at an angle of 120 degrees. To find the x component (F_clare_x), we use the formula F_clare_x = F_clare * cos(angle).

F_clare_x = 200 N * cos(120 degrees) = 200 N * -0.5 = -100 N

And for the y component (F_clare_y), we use the formula F_clare_y = F_clare * sin(angle).

F_clare_y = 200 N * sin(120 degrees) = 200 N * 0.866 = 173.2 N

Now let's add up the x and y components of both forces to get the overall x and y components of the resultant force.

Resultant force (F_resultant_x) = F_emily_x + F_clare_x = 60 N + (-100 N) = -40 N

Resultant force (F_resultant_y) = F_emily_y + F_clare_y = 103.92 N + 173.2 N = 277.12 N

To find the magnitude (F_resultant) and the direction (angle_resultant) of the resultant force, we can use the Pythagorean theorem and trigonometry.

F_resultant = sqrt(F_resultant_x^2 + F_resultant_y^2)

F_resultant = sqrt((-40 N)^2 + (277.12 N)^2) = sqrt(1600 N^2 + 76668.6144 N^2) = sqrt(78268.6144 N^2) = 279.43 N (rounded to two decimal places)

angle_resultant = arctan(F_resultant_y / F_resultant_x)

angle_resultant = arctan(277.12 N / -40 N) = arctan(-6.928) = -81.87 degrees (rounded to two decimal places)

So, the magnitude of the resultant force is approximately 279.43 N, and the direction is approximately -81.87 degrees. Keep in mind that the negative sign indicates the resultant force is in the opposite direction of the line between the centers of the two goals.

And there you have it! Now let's hope no one gets clown-footed during the soccer match!

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)

280N

To calculate the magnitude and direction of the resultant force, we need to determine the x and y components of the forces and then combine them.

First, let's find the x and y components of Emily's force:

The x component of Emily's force (F_emily_x) can be calculated using the formula:
F_emily_x = F_emily * cos(angle_emily)
where F_emily is the magnitude of Emily's force and angle_emily is the angle at which she kicks the ball.

Substituting the values:
F_emily_x = 120 N * cos(60 degrees)
F_emily_x = 120 N * 0.5
F_emily_x = 60 N

The y component of Emily's force (F_emily_y) can be calculated using the formula:
F_emily_y = F_emily * sin(angle_emily)
where F_emily is the magnitude of Emily's force and angle_emily is the angle at which she kicks the ball.

Substituting the values:
F_emily_y = 120 N * sin(60 degrees)
F_emily_y = 120 N * (√3/2)
F_emily_y = 60√3 N

Now, let's find the x and y components of Clare's force:

The x component of Clare's force (F_clare_x) can be calculated using the formula:
F_clare_x = F_clare * cos(angle_clare)
where F_clare is the magnitude of Clare's force and angle_clare is the angle at which she kicks the ball.

Substituting the values:
F_clare_x = 200 N * cos(120 degrees)
F_clare_x = 200 N * (-0.5)
F_clare_x = -100 N

The y component of Clare's force (F_clare_y) can be calculated using the formula:
F_clare_y = F_clare * sin(angle_clare)
where F_clare is the magnitude of Clare's force and angle_clare is the angle at which she kicks the ball.

Substituting the values:
F_clare_y = 200 N * sin(120 degrees)
F_clare_y = 200 N * (√3/2)
F_clare_y = 100√3 N

Now, let's combine the x and y components of the forces to find the resultant force.

The x component of the resultant force (F_resultant_x) is the sum of the x components of Emily's and Clare's forces:
F_resultant_x = F_emily_x + F_clare_x
F_resultant_x = 60 N + (-100 N)
F_resultant_x = -40 N

The y component of the resultant force (F_resultant_y) is the sum of the y components of Emily's and Clare's forces:
F_resultant_y = F_emily_y + F_clare_y
F_resultant_y = 60√3 N + 100√3 N
F_resultant_y = 160√3 N

To find the magnitude of the resultant force (F_resultant), we can use the Pythagorean theorem:
F_resultant = √(F_resultant_x² + F_resultant_y²)
F_resultant = √((-40 N)² + (160√3 N)²)
F_resultant = √(1600 N² + 25600 N²)
F_resultant = √27200 N²
F_resultant ≈ 165.28 N

The direction of the resultant force (θ_resultant) can be found using the inverse tangent function:
θ_resultant = arctan(F_resultant_y / F_resultant_x)
θ_resultant = arctan((160√3 N) / (-40 N))
θ_resultant ≈ arctan(-4√3)
θ_resultant ≈ -75.96 degrees

Therefore, the magnitude of the resultant force is approximately 165.28 N, and the direction of the resultant force is approximately -75.96 degrees, measured from the line between the centers of the two goals.