Question

A ball is projected upwards from ground it is observed from 73.5 metre Hai window twice at the interval of 2 seconds answer the following for the motion of the ball (take g = 9.8 m/s^2)
1. What is the velocity of projection for the ball?
2. The maximum height attained by the ball above the ground is?
3. Total time of flight of the ball is?

Answer 1

Let maximum height attained by ball is H m when we throw the ball with speed u m/s.at maximum height velocity of ball = 0

a/c to question,

73.5m heigh window are observed twice at the interval 2 sec.

Let first time after t sec we observe the window and then after (t + 2)sec we observe it once again.

using formula, s = ut + 1/2 at²

73.5 = ut + 1/2 × (-g)t²

or, 73.5 = ut - 4.9t²

or, 4.9t² - ut + 73.5 = 0....(1) , t and (t + 2) is the zeros of this polynomial.

so, (t + t + 2) = u/4.9

t(t + 2) = 73.5/4.9 = 15

now, difference of roots = (t + 2) - t = 2 = √{(t + 2 + t)² - 4t(t + 2)}

or, 2 = √{u²/4.9² - 4 × 15}

or , 4 = u²/4.9² - 60

or, 64 = 8² = (u/4.9)²

or, u = 8 × 4.9 = 39.2 m/s

velocity of projection for the ball = 39.2m/s

now, height attained by ball , H = u²/2g

= (39.2)²/2(9.8)

= 78.4 m

total time of flight , T = 2u/g

= 2 × 39.2/9.8

= 8sec

Answer 2

Let maximum height attained by ball is H m when we throw the ball with speed u m/s.at maximum height velocity of ball = 0

a/c to question,

73.5m heigh window are observed twice at the interval 2 sec.

Let first time after t sec we observe the window and then after (t + 2)sec we observe it once again.

using formula, s = ut + 1/2 at²

73.5 = ut + 1/2 × (-g)t²

or, 73.5 = ut - 4.9t²

or, 4.9t² - ut + 73.5 = 0....(1) , t and (t + 2) is the zeros of this polynomial.

so, (t + t + 2) = u/4.9

t(t + 2) = 73.5/4.9 = 15

now, difference of roots = (t + 2) - t = 2 = √{(t + 2 + t)² - 4t(t + 2)}

or, 2 = √{u²/4.9² - 4 × 15}

or , 4 = u²/4.9² - 60

or, 64 = 8² = (u/4.9)²

or, u = 8 × 4.9 = 39.2 m/s

velocity of projection for the ball = 39.2m/s

now, height attained by ball , H = u²/2g

= (39.2)²/2(9.8)

= 78.4 m

total time of flight , T = 2u/g

= 2 × 39.2/9.8

= 8sec