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Motion In Straight Line

Question
CBSEENPH11017077

A ball is thrown vertically upward and returns back to the hands of thrower in 6s. Find the velocity of throw and maximum height attained by the ball.

Solution
Let the ball be projected with velocity u from the ground.
Let us take upward direction positive and ground as reference point.
Thus,
Displacement comma space straight y subscript 0 equals 0 comma space space straight y space equals space 0

straight g space equals space minus 9.8 space straight m divided by straight s squared

Time space of space travel comma space straight t equals 6 straight s 
Now, using the formula,
    straight y space equals straight y subscript 0 plus u t plus 1 half a t squared 
rightwards double arrow  0 equals 0 plus straight u cross times 6 plus 1 half left parenthesis negative 9.8 right parenthesis left parenthesis 6 right parenthesis squared
rightwards double arrow     0 = 6u-176.4
i.e.,      u = 29.4 m/s
Let h be the maximum height attained by the ball.
Using third equation of motion, we have
therefore space space space space straight v squared minus straight u squared equals 2 a s 
rightwards double arrow  (0)- (29.4)= 2 x(-9.8)h
rightwards double arrow     h = 44.1 m, is the maximum height attained by the ball.