Answer:
about 0.1133 m/s 66.4° below horizontal, to the left
Step-by-step explanation:
You want the acceleration of a 25 kg mass with forces of 4.0 N and 6.5 N acting in the directions shown.
Resultant
The sum of the two forces is about 2.832 N in the direction to the left 66.4° below horizontal. The diagram of forces is the first attachment.
The acceleration is given by ...
a = F/m = (2.832 N)/(25 kg) ≈ 0.1133 m/s
The acceleration of the mass is about 0.1133 m/s to the left at an angle 66.4° below horizontal.
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Additional comment
We like a vector calculator for doing this sort of math. If you're doing this "by hand" without making use of the vector capabilities of your calculator, you can do it several ways. One way is to add the horizontal and vertical components of the forces:
- horizontal force = 2√3 -3.25√2 ≈ -1.1321
- vertical force = 2 -3.25√2 ≈ -2.5962
Then the acceleration is the Pythagorean sum, divided by the mass:
a = √(1.1321² +2.5962²)/25 ≈ (√8.0219)/25 ≈ 0.1133 m/s
Another way to find the resultant force is to solve the triangle of forces using the law of cosines.
r = √(6.5² +4.0² -2·6.5·4.0·cos(15°)) ≈ √8.0219 N
Either way, you need a calculator, so you may as well make full use of its capability.