A ball is moving in a circular path of radius 5 ~m . If tangential acceleration at any instant is 10 ~ms ⁻² and the net acceleration makes an angle of 30^ with the centripetal acceleration, then, the instantaneous speed is

Step-by-step solution

The tangential acceleration is given as a_t = 10 ~ms ⁻² . The centripetal acceleration is given by a_c = v^2 r , where v is the instantaneous speed and r = 5 ~m . Thus, a_c = v^2 5 . The net acceleration a is the vector sum of the tangential acceleration a _t and the centripetal acceleration a _c . Since a _t and a _c are perpendicular, the angle between the net acceleration a and the centripetal acceleration a _c is given by = a_t a_c . Given = 30^ , we have 30^ = 1 3 . Substituting the values, 1 3 = 10 v^2 / 5 =