a student uses the equation $\tan\theta=\frac{s^{2}}{4g}$ to represent the speed, s, in feet per second, of…

a student uses the equation $\tan\theta=\frac{s^{2}}{4g}$ to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline $\theta$, where $sin\theta = \frac{1}{2}$. to solve the problem, the student used the given value of $sin\theta$ to find the value of $\tan\theta$ and then substituted the value of $\tan\theta$ in the equation above to solve for s. what is the approximate value of s, the speed of the car in feet per second?\no 5.3\no 7.5\no 9.2\no 28.3

a student uses the equation $\tan\theta=\frac{s^{2}}{4g}$ to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline $\theta$, where $sin\theta = \frac{1}{2}$. to solve the problem, the student used the given value of $sin\theta$ to find the value of $\tan\theta$ and then substituted the value of $\tan\theta$ in the equation above to solve for s. what is the approximate value of s, the speed of the car in feet per second?\no 5.3\no 7.5\no 9.2\no 28.3

Answer

Explanation:

Step1: Find cosθ

Given $\sin\theta=\frac{1}{2}$, using $\sin^{2}\theta+\cos^{2}\theta = 1$, we have $\cos\theta=\sqrt{1 - (\frac{1}{2})^{2}}=\frac{\sqrt{3}}{2}$.

Step2: Find tanθ

$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}$.

Step3: Solve for s

Substitute $\tan\theta$ into $\tan\theta=\frac{s^{2}}{4g}$ (assuming $g = 32$ ft/s²). $\frac{1}{\sqrt{3}}=\frac{s^{2}}{4\times32}$, then $s^{2}=\frac{4\times32}{\sqrt{3}}$, $s=\sqrt{\frac{128}{\sqrt{3}}}\approx 9.2$.

Answer:

9.2