Question

(5 pts) evaluate the following function for when $l = 2m$. $v(l)=sqrt{\frac{330 kg\frac{m}{s^{2}}}{\frac{1.4 kg}{2m}}}$
(5 pts) convert the angle, $107^{circ}$, from degrees to radians. $107^{circ}\times\frac{2pi}{360^{circ}}approx0.59pi$

Explanation:

3.

Step1: Substitute \(l = 2m\) into the function

\[v(l)=\sqrt{\frac{330\frac{kg\cdot m}{s^{2}}}{\frac{1.4kg}{l}}}\] becomes \[v(2)=\sqrt{\frac{330\frac{kg\cdot m}{s^{2}}}{\frac{1.4kg}{2m}}}\]

Step2: Simplify the denominator - numerator operation

\[v(2)=\sqrt{330\frac{kg\cdot m}{s^{2}}\times\frac{2m}{1.4kg}}=\sqrt{\frac{330\times2}{1.4}\frac{m^{2}}{s^{2}}}=\sqrt{471.43\frac{m^{2}}{s^{2}}}\]

Step3: Calculate the square - root

\[v(2)\approx21.71\frac{m}{s}\]

Step1: Use the conversion formula

The formula to convert degrees to radians is \(\theta_{rad}=\theta_{deg}\times\frac{2\pi}{360^{\circ}}\). Substitute \(\theta_{deg} = 107^{\circ}\) into the formula: \(\theta_{rad}=107^{\circ}\times\frac{2\pi}{360^{\circ}}\)

Step2: Simplify the expression

\(\theta_{rad}=\frac{107\pi}{180}\approx1.87\) radians (or if we want to keep in terms of \(\pi\) as in the wrong - start of the original work, \(\theta_{rad}=\frac{107}{180}\times2\pi=\frac{107\pi}{90}\approx1.19\pi\) radians)

Answer:

\(v(2)\approx21.71\frac{m}{s}\)

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