Question

A Cyclist goes round a circular path of radius 20m with a speed of 14ms. Find the angele through which his cycle make the vertical (g-9.8ms) ​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Radius, r = 20 m

• Speed, v = 14 m/s

• Acceleration, g = 9.8 m/s²

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Angel, theta

$\;\;\underline{\textbf{\textsf{Solution :-}}}$

$\underline{\:\textsf{As we know the formula :}}$

$\sf Speed = \sqrt{Radius \times Acceleration \times \tan(\theta)}$

$\underline{\:\textsf{Now, put the given values in the formula :}}$

$\\\\\longrightarrow \sf14= \sqrt{20 \times 9.8 \times \tan(\theta)} \\\\\\\longrightarrow \sf {(14)}^{2} = 196 \times \tan(\theta)\\\\\\\longrightarrow \sf196 = 196 \times \tan(\theta)\\\\\\\longrightarrow \sf1 = \tan(\theta) = 45^{ \circ} \\\\\\\longrightarrow \sf \theta = 45^{ \circ}$

$\;\;\underline{\textbf{\textsf{ Hence -}}}$

⠀

$\underline{\textsf{Angle through cyclist make vertical curve is \textbf{45 ^{\circ} }}}.$

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Answer 2

Hope it helps to you......