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Mekhanik [1.2K]
3 years ago
13

If a vector a - b = 2c, a + b = 4c and c = 3i + 4j,find a and b

Physics
1 answer:
iren [92.7K]3 years ago
6 0
Ans:
a = 9i + 12j
b = 3i + 4j

Explanation:
We have two equations:

<span>a - b = 2c --- (A)
</span><span>a + b = 4c --- (B)

and two unknowns:
a = ?
b = ?

Whereas,
c = 3i + 4j

Add equations (A) and (B):
=> a - b = 2c
     a + b = 4c
----------------------
    2a = 6c

=> a = 3c --- (C)
Put the value of vector c in equation (C):

(C) => a = 3(3i + 4j)
=> a = 9i + 12j

Now that we have vector a, put that vector and vector c in equation (A):
(A)=> (9i + 12j) - b = 2(3i + 4j)

=> b = (9i + 12) - (6i + 8j)
=> b = 3i + 4j

Ans:
a = </span>9i + 12j
b = 3i + 4j<span>

</span>
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How much force is needed to accelerate a 20 kg mass at a rate of 4 m/s to the second power?
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A pendulum has a length of 2 m and a 30 kg mass hanging on the end. What is the period of the
anastassius [24]

Answer:

T = 2.83701481512 seconds

Explanation:

Hi!

The formula that you will want to use to solve this question is:

T = 2\pi *\sqrt{\frac{L}{g}  }

T--> period

L --> length of the pendulum

g --> acceleration due to gravity (9.8m/s^2)

since we know that the mass of the bob at the end of the pendulum does not affect the period of the pendulum, we can go ahead and ignore that bit of information (unless, of course, the weight causes the pendulum to stretch)

so now we can plug in our given info into the formula above and solve!

T = 2*pi * sqrt(2/9.8)

T = 2.83701481512 seconds

*Note*

- I used 3.14 to pi, if you need to use a different value for pi (a longer version, etc) your answer will be slightly different

I hope this helped!

7 0
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Answer:

Fractional error = 0.17

Percent error = 17%

F = 112 ± 19 N

Explanation:

Plug in the values to find the force:

F = (3.5 kg) (20 m/s)² / (12.5 m) = 112 N

Find the fractional error:

ΔF/F = Δm/m + 2Δv/v + Δr/r

ΔF/F = 0.1/3.5 + 2(1/20) + 0.5/12.5

ΔF/F = 0.17

Multiply by 100% to find the percent error:

ΔF/F × 100% = 17%

Solve for the absolute error:

ΔF = 0.17 × 112 N = 19 N

Therefore, the force is:

F = 112 ± 19 N

8 0
3 years ago
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