Question

A car is moving forward at 0.35 m/s. Attached to the rear-view mirror is a small air freshener with a string that is 15 cm

long. If the car were to suddenly come to a complete stop. What would be the maximum angle the air freshener string
would rotate through from a starting position of directly down?

Answer 1

`16.6^(o)`

Step-by-step explanation:

From the law of conservation of energy, the potential energy is converted to kinetic energy hence

`mgh=0.5mv^(2)` where m is mass, g is acceleration due to gravity considered as 9.1m/s2, h is height and v is the velocity

`gh=0.5v^(2)` and making h is the subject

`h=0.5v^(2)/g=0.5(0.35^(2))/9.81= 0.006244 m or 0.6244 cm`

Also,
`h=L-Lcos\theta` where L is the length of string given as 15 cmand
`\theta` is the angle of inclination

`h=L(1-cos\theta)`

`1-cos\theta=\frac {h}{L}=\frac {0.6244}{15}=0.041624`

`cos\theta=1-0.041624=0.958376`

`\theta=cos^(-1)(0.958376)= 16.58932^(o)`

Therefore,
`\theta` is approximately
`16.6^(o)`