Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 65.0ú. Dog " A" exerts a force of 256 N and dog " B " exerts a force of 344 N .
I) Find the magnitude of the resultant force. ( Answered = 508 N )
II) Find the angle the resultant force makes with dog "A" 's rope.
I want the answer for quistion (II) as soon as possible .. please .. Thank you :)
You want the answer?
I will be happy to critique your work. YOu have two sides and the included angle. I would use the law of cosines to find the third side (resultant), and then the law of sines to find the other angles.
You will find the sketch of this problem will be a great assist in the solution.
LMAO BOBPURSLEY'S BEING SARCASTIC LOLOLOL he's getting back at kuwaiti cuz kuwaiti did him dirty on the exact same problem by being vague and unhelpful
Fr=256[0o] + 344[65o]=256 + 145.4+311.8i
= 401.4 + 311.8i = 508N.[37.8o] N. of E.
= 37.8o N. of dog "A".
I apologize if my previous response was not clear enough. Here's a step-by-step explanation of how to find the angle between the resultant force and Dog A's rope:
1. Draw a sketch of the problem, showing Dog A, Dog B, and the post.
2. Label the forces exerted by Dog A and Dog B as A and B, respectively, with their respective magnitudes (A = 256 N, B = 344 N).
3. Determine the direction of each force. In this case, since the dogs are pulling horizontally, both forces will be in the same direction.
4. Use the law of cosines to find the magnitude of the resultant force (R) using the equation:
R^2 = A^2 + B^2 - 2ABcos(θ)
where θ is the angle between the forces A and B. In this case, θ = 65.0°.
Substituting the values:
R^2 = (256 N)^2 + (344 N)^2 - 2(256 N)(344 N)cos(65.0°)
5. Calculate R:
R = √[ (256 N)^2 + (344 N)^2 - 2(256 N)(344 N)cos(65.0°) ]
6. Calculate the angle between the resultant force (R) and Dog A's rope (angle α):
To find α, we can use the law of sines:
sin(α) / R = sin(θ) / B
Substituting the known values:
sin(α) / R = sin(65.0°) / 344 N
Now solve for sin(α):
sin(α) = (R / 344 N) * sin(65.0°)
7. Calculate α:
α = sin^(-1)[ (R / 344 N) * sin(65.0°) ]
8. Substitute the value of R (found in step 5) into the equation in step 7, and calculate α:
α = sin^(-1)[ (508 N / 344 N) * sin(65.0°) ]
9. Evaluate α using a calculator:
α ≈ 65.75°
So, the angle between the resultant force and Dog A's rope is approximately 65.75°.