The 1st row has 15 chairs.
The 2nd row has 15 + 3 = 18 chairs.
The 3rd row has 18 + 3 = 15 + 2•3 = 21 chairs.
The 4th row has 21 + 3 = 15 + 3•3 = 24 chairs.
The pattern continues, so that the n-th row has 15 + (n - 1)•3 = 3n + 12 chairs.
If there are 15 rows, then the total number of chairs is
where we use the formulas
By conservation of momentum,
(900 kg) (15.0 m/s) i + (750 kg) (20.0 m/s) j = (900 kg + 750 kg) v
where v is the velocity vector of the combined cars. Solve for v :
(13,500 i + 15,000 j) kg•m/s = (1650 kg) v
v ≈ (8.18 i + 9.09 j) m/s
Then the direction of v relative to East is θ such that
tan(θ) ≈ 9.09/8.18 ⇒ θ ≈ 48.0°
so the wreckages would move at approximately 48.0° north of east.
Answer:
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Explanation:
