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15 m/s=4π rad/s×r×sin⁡(15∘)15\,\text{m/s} = 4\pi\,\text{rad/s} \times r \times \sin(15^\circ)

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Q. 15 m/s=4π rad/s×r×sin⁡(15∘)15\,\text{m/s} = 4\pi\,\text{rad/s} \times r \times \sin(15^\circ)
  1. Write Equation: Write down the given equation.\newlineWe are given the equation 15 m/s=4π rad/s×r×sin⁡(15°)15 \, \text{m/s} = 4\pi \, \text{rad/s} \times r \times \sin(15°). We need to solve for rr.
  2. Isolate r: Isolate r in the equation.\newlineTo find r, we need to divide both sides of the equation by 4π rad/s4\pi \, \text{rad/s} and sin⁡(15°)\sin(15°).\newliner=15 m/s4π rad/s×sin⁡(15°)r = \frac{15 \, \text{m/s}}{4\pi \, \text{rad/s} \times \sin(15°)}
  3. Calculate sin⁡(15∘)\sin(15^\circ): Calculate sin⁡(15∘)\sin(15^\circ). Using a calculator or trigonometric tables, we find that sin⁡(15∘)\sin(15^\circ) is approximately 0.25880.2588.
  4. Substitute sin⁡(15°)\sin(15°): Substitute sin⁡(15°)\sin(15°) into the equation.r=15 m/s4π rad/s×0.2588r = \frac{15 \, \text{m/s}}{4\pi \, \text{rad/s} \times 0.2588}
  5. Perform Calculation: Perform the calculation.\newliner=15 m/s4π×0.2588 rad/sr = \frac{15 \, \text{m/s}}{4\pi \times 0.2588 \, \text{rad/s}}\newliner≈15 m/s3.1416×0.2588 rad/sr \approx \frac{15 \, \text{m/s}}{3.1416 \times 0.2588 \, \text{rad/s}}\newliner≈15 m/s0.8135 rad/sr \approx \frac{15 \, \text{m/s}}{0.8135 \, \text{rad/s}}\newliner≈18.44 mr \approx 18.44 \, \text{m}

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