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A ball is tossed vertically into the air with an initial speed somewhere between (25 - ∈) m/s and (25 + ∈) m/s, where ∈ is a small number compared to 25. The total time of flight for the ball to return to the ground will be somewhere between t - T and t + T. Find t and T.

A  ball  is  tossed   vertically   into  the  air  with  an initial   speed somewhere   between (25 - ∈) m/s and (25 + ∈) m/s, where ∈ is a small  number  compared  to 25. The  total time of flight for the  ball  to  return  to  the  ground  will  be  somewhere   between t -  T and t + T. Find t and T.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
Assumptions:
Assume that the time of flight for the ball is and the time taken by the ball to reach the highest point be t1.
Ignore the effect of air resistance on the ball, such that the ball experiences the acceleration equal to free fall acceleration.
Given: 235-314_1.PNG
The negative sign of the g accounts for the fact that the direction of the acceleration is opposite to that of the initial velocity vector.
The time of flight of the ball is twice the time t1 and is given as

235-1007_1.PNG
235-922_1.PNG
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