Two forces of 7 lb. and 14 lb. act on a body at right angles to each other. Find their resultant. Find the angle their resultant force makes with the force of 14 lb.

The resultant is the hypotenuse of the force vector triangle,

sqrt(49 + 196) = ___

The angle of the resultant force with respect to the 14 lb force is
arctan 1/2 = ___ degrees.

ftr

To find the resultant force of the two forces acting at right angles, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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, the two forces acting at right angles are 7 lb and 14 lb. Let's call the force of 7 lb as F1 and the force of 14 lb as F2.

Using the Pythagorean theorem:
Resultant force^2 = F1^2 + F2^2

Substituting the values of F1 and F2:
Resultant force^2 = (7 lb)^2 + (14 lb)^2
Resultant force^2 = 49 lb^2 + 196 lb^2
Resultant force^2 = 245 lb^2

Taking the square root of both sides:
Resultant force = square root of 245 lb^2
Resultant force ≈ 15.66 lb (rounded to two decimal places)

So, the resultant force of the two forces is approximately 15.66 lb.

To find the angle that the resultant force makes with the force of 14 lb, we can use trigonometry. Specifically, we can use the sine function.

The sine of an angle in a right-angled triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

Let's call the angle between the resultant force and the force of 14 lb as θ.

Using the sine function:
sin(θ) = opposite / hypotenuse

Substituting the values:
sin(θ) = F1 / Resultant force
sin(θ) = 7 lb / 15.66 lb
sin(θ) ≈ 0.447

To find the angle θ, we need to take the inverse sine (also called arcsine) of 0.447.

arcsin(0.447) ≈ 27.46 degrees

Therefore, the angle that the resultant force makes with the force of 14 lb is approximately 27.46 degrees.

To find the resultant force of the two forces acting on the body, 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 have two forces acting at a right angle to each other. Let's call the force of 7 lb. "F1" and the force of 14 lb. "F2."

To find the resultant force, we can use the formula:

Resultant force = √(F1^2 + F2^2)

Plugging in the values, we have:

Resultant force = √(7^2 + 14^2)
= √(49 + 196)
= √(245)
≈ 15.65 lb.

So, the magnitude of the resultant force is approximately 15.65 lb.

To find the angle that the resultant force makes with the force of 14 lb., we can use the trigonometric function tangent (tan). The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let's call the angle we're looking for "θ."

The formula for finding the angle θ is:

θ = tan^(-1)(F1/F2)

Plugging in the values, we have:

θ = tan^(-1)(7/14)
= tan^(-1)(0.5)
≈ 26.57°

So, the angle that the resultant force makes with the force of 14 lb. is approximately 26.57°.