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A  all thrown upwards returns to the ground with the initial speed of u. The ball is at the height of 80 m at two times the time interval being 6 seconds. Find u, by assuming g=10m/s^2. (Please explain with diagram)
Asked by acv27joy | 19 May, 2018, 07:03: PM
we need to apply the equation " S = u×t-(1/2)g×t2 "

80 = u×t-(1/2)×g×t= u×t-(1/2)×10×t2 ;

Above equation is rewritten as t2 - (u/5)t + 16 =0 ................(1)

Solution for t from the quadratic equation, which has two roots,  gives the two instance of time when the ball is at a height of 80 m.
One value of time is during ascending and another is during descending.

the constant coefficent 16 of eqn.(1) is product of two numbers and these two numbers differ by 6.
we have two numbers 2 and 8, satisfying this condition

hence eqn(1) is of the form (t-2)(t-8) = t2-10t+16 = 0 ................(2)

if we compare (1) and (2), we get u = 50 m/s
Answered by Thiyagarajan K | 20 May, 2018, 11:41: AM

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