Two forces of 7 lb. and 14 lb. act on a body at right angles to each other. Find the angle their resultant force makes with the force of 14 lb.
Isn't this a right triangle?
TanTheta=7/14
theta = arctan .5= ....
This is hardly calculus
14
To find the angle that the resultant force makes with the force of 14 lb, we can use trigonometry.
First, let's draw a diagram to visualize the forces. We have two forces, one of 7 lb and the other of 14 lb, acting at right angles to each other. Let's call the force of 7 lb as F1 and the force of 14 lb as F2.
Now, let's calculate the magnitude of the resultant force (F_r), which is the total force resulting from the combination of F1 and F2. We can use the Pythagorean theorem to find F_r:
F_r^2 = F1^2 + F2^2
F_r^2 = 7^2 + 14^2
F_r^2 = 49 + 196
F_r^2 = 245
F_r = sqrt(245)
F_r ≈ 15.65 lb (rounded to two decimal places)
So, the magnitude of the resultant force is approximately 15.65 lb.
Next, let's find the angle that the resultant force makes with the force of 14 lb. We can use trigonometric ratios to determine this angle.
cosθ = F1 / F_r
cosθ = 7 / 15.65
θ ≈ cos^(-1)(7/15.65)
θ ≈ 64.05 degrees (rounded to two decimal places)
Therefore, the angle between the resultant force and the force of 14 lb is approximately 64.05 degrees.