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Answer:
[tex]v = 23.88m/s[/tex]
Explanation:
Given
[tex]r = 225m[/tex]
[tex]\theta = 14.5^\circ[/tex]
Required: Determine the speed of the train
To solve this question, we apply the concept of tension.
Let the tension on the cord be T.
Tension is calculated as:
[tex]T = mg[/tex]
So, the tensions acting on the system are:
[tex]T*sin(\theta) = \frac{mv^2}{r}[/tex] and
[tex]T*cos(\theta) = mg[/tex]
Divide the equations by one another
[tex]\frac{T*sin(\theta)}{T * cos(\theta)} = \frac{mv^2}{mgr}[/tex]
[tex]\frac{sin(\theta)}{cos(\theta)} = \frac{v^2}{gr}[/tex]
[tex]tan(\theta) = \frac{v^2}{gr}[/tex]
Make v^2 the subject
[tex]v^2 = grtan(\theta)[/tex]
Take the square root of both sides
[tex]v = \sqrt{grtan(\theta)[/tex]
Substitute values for g (9.8), r 225 and [tex]\theta[/tex] (14.5)
[tex]v = \sqrt{9.8 * 225 * tan(14.5^\circ)}[/tex]
[tex]v = \sqrt{9.8 * 225 * 0.2586}[/tex]
[tex]v = \sqrt{570.213}[/tex]
[tex]v = 23.88m/s[/tex]
Hence, the trains' velocity is approximately 23.88m/s