Question

A train is travelling along a curve of radius 700 at 21 km/hr, find angle in radian through which train turns in 2 minutes​

Answer 1

Given :

The Radius of the curve path = r = 700 m

The speed of the train = s = 21 km/hr = 350 m/min

The time for train to turn curve = t = 2 min

Too Find :

The angle in radian through which train turns in 2 minutes​

Solution :

Let The length of arc = distance cover by train = L meters

∵  Distance = Speed ×Time

So ,     length of arc =  speed of the train ×  time for train to turn

                                = 350 m/min × 2 min

                                = 700 meters

Now,

∵    length of arc = $\dfrac{\Theta }{360^{\circ}}$ × 2 × π × radius

Or,            700 m = $\dfrac{\Theta }{360^{\circ}}$ × 2 × 3.14 × 700 m

Or,             $\dfrac{\Theta }{360^{\circ}}$  = $\dfrac{700}{4396}$

Or,               Ф    =  $\dfrac{700}{4396}$ × 360

                          = 57.32°

Again

∵   180°  =  π radian

∴    57.32°= $\dfrac{\pi }{180^{\circ}}$ ×  57.32° radian

               =  $\dfrac{3.14}{180^{\circ}}$ ×  57.32° radian

              = 0.99 radian

Hence, The angle in radian through which train turns in 2 minutes is 0.99 radian . Answer​