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COMEDK2023Evening ShiftPhysicsMotion in Two DimensionsActual

A hockey player hits the ball at an angle of 37^ from the horizontal with an initial speed of 40 ~m / s (a right angled triangle with one of the angle is 37^ and their sides in the ratio of 6: 8: 10 ). Assume that the ball is in a vertical plane. The time at which the ball reaches the highest point of its path is

Options

  1. A3.2 s
  2. B2.4 s
  3. C0.32 s
  4. D0.24 s

Correct answer

B. 2.4 s

Step-by-step solution

The initial velocity of the ball is u = 40 m/s and the angle of projection is = 37^ . The vertical component of the initial velocity is given by u_y = u . Given the triangle with sides in ratio 3:4:5 (which is equivalent to 6:8:10 ), 37^ = 3 5 . Substituting the values, u_y = 40 3 5 = 8 3 = 24 m/s . At the highest point of the trajectory, the vertical component of the velocity becomes zero, v_y = 0 . Using the equation of motion v_y = u_y - gt , where g = 10 m/s ^2 is the acceleration due to gravity: 0 = 24 - 10t 1

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