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A ball is thrown vertically upward with a velocity 10m/s and it returns the ground with speed 8m/s . There exist a constant air resistance . The maximum height attained by ball is

A ball is thrown vertically upward with a velocity 10m/s and it returns the ground with speed 8m/s . There exist a constant air resistance . The maximum height attained by ball is

Grade:11

1 Answers

Deepak Kumar
31 Points
6 years ago
Initial speed of ball = U0 = 10m/s.
Final speed of ball = Uf = 0m/s (at maximum height).
Gravitational acceleration = g = 9.8m/s (In downward direction).
Let maximumum Height cover by ball = H.
Let accileration due to Air resistance working on it = R.
So apply kinematics 3rd equation from ground to maximum height.
    V2 = U2 + 2*a*H
     02 = (10)2 +2*(-g-R)*H.
  so, g+R = 50/H  ------------------(1)
 
Now apply kinematics 3rd equation from maximum height to ground.
      82= 02 + 2*(g-R)*H.
   So, g-R = 32/H ------------------(2)
Adding equation 1st and 2nd , we get
      H = 82/(2*g) = 82/(2*9.8) = 4.18367m.

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