Sue and Jenny kick a soccer ball at exactly the same time. Sue’s foot exerts a force of 49.9 N to the north. Jenny’s foot exerts a force of 119.7 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. Fr^2 = 119.7^2 + 49.9^2 = 16,818.1
Fr = 129.7 N.
b. tanA = Y/X = 49.9/119.7 = 0.41688
A = 22.63o = Direction.
a) The magnitude of the resultant force can be calculated using the Pythagorean theorem. Let's call the force Sue exerts "Fsue" and the force Jenny exerts "Fjenny".
Fsue = 49.9 N (north)
Fjenny = 119.7 N (east)
Using the Pythagorean theorem,
Resultant force = sqrt(Fsue^2 + Fjenny^2)
Resultant force = sqrt((49.9 N)^2 + (119.7 N)^2)
Resultant force = sqrt(2490.01 N^2 + 14328.09 N^2)
Resultant force = sqrt(16818.1 N^2)
Resultant force ≈ 129.7 N
Therefore, the magnitude of the resultant force on the ball is approximately 129.7 N.
b) To find the direction of the resultant force, we can use inverse tangent.
Direction = atan(Fjenny/Fsue)
Direction = atan(119.7 N / 49.9 N)
Direction ≈ 68.5 degrees
Therefore, the direction of the resultant force (measured from East) is approximately 68.5 degrees.
To find the magnitude of the resultant force on the ball, we can use the Pythagorean theorem.
Let's label the forces:
Sue's force: 49.9 N to the north
Jenny's force: 119.7 N to the east
Using the Pythagorean theorem, the magnitude of the resultant force (R) can be calculated as follows:
R^2 = (49.9 N)^2 + (119.7 N)^2
R^2 = 2490.01 N^2 + 14336.09 N^2
R^2 = 16826.1 N^2
R = √16826.1 N
R ≈ 129.7 N
Therefore, the magnitude of the resultant force on the ball is approximately 129.7 N.
To find the direction of the resultant force, we can use trigonometry.
The direction of the resultant force can be found using the equation:
θ = tan^(-1)(opposite/adjacent)
Here, the opposite side is 49.9 N (Sue's force to the north) and the adjacent side is 119.7 N (Jenny's force to the east).
θ = tan^(-1)(49.9/119.7)
θ ≈ 22.34°
Therefore, the direction of the resultant force (measured from East) is approximately 22.34°.
To find the magnitude of the resultant force on the ball, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the northward force exerted by Sue's foot (49.9 N) as one side of the triangle, and the eastward force exerted by Jenny's foot (119.7 N) as the other side. The resultant force can be considered as the hypotenuse.
Using the Pythagorean theorem:
Resultant force^2 = Sue's force^2 + Jenny's force^2
Resultant force^2 = (49.9 N)^2 + (119.7 N)^2
Calculating the squares:
Resultant force^2 = 2490.01 N^2 + 14304.09 N^2
Resultant force^2 = 16794.1 N^2
Taking the square root of both sides to find the resultant force:
Resultant force = √(16794.1 N^2)
Resultant force ≈ 129.6 N
So, the magnitude of the resultant force on the ball is approximately 129.6 N.
To find the direction of the resultant force, we can use the trigonometric concept of inverse tangent (tan⁻¹). The inverse tangent function can give us the angle given the opposite and adjacent sides of a right triangle.
In this case, we have the eastward force (119.7 N) as the adjacent side, and the northward force (49.9 N) as the opposite side.
Using the inverse tangent function:
Angle = tan⁻¹(opposite/adjacent)
Angle = tan⁻¹(49.9 N/119.7 N)
Calculating the angle:
Angle ≈ 23.7°
So, the direction of the resultant force (measured from East) is approximately 23.7°.