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CBSE Class 11-science Answered

A ball is thrown vertically upwards with speed of 10m/s from the top of the tower 200m high and another is thrown vertically downwards with the same speed simultaneously.the time difference between them in reaching the ground in seconds(g=10m/s²)  
Asked by Sachinkumarrayray7755 | 22 Jun, 2018, 02:58: PM
answered-by-expert Expert Answer
To find the height h reached by the ball thrown vertically, we need to use the formula "v2 = u2 - 2gh ",
with final velocity v = 0, initial velocity u = 10 m/s and g = 10 m/s2
 
hence h = u2 / 2g = (10×10) /(2×10) = 5 m
 
Time t to reach the highest point will be obtained from the formula " v= u-gt ", with v=0; hence time t = u/g = 10/10 = 1 s ;
 
After reaching the height h, the ball falls to the ground under gravity.
 
Time to reach ground will be obtained from the formula " S = ut+(1/2)gt2 ", here initial velocity u = 0 and S = (200+5) m; let this time be t1
 
hence 205 = (1/2)×10×t1 ; we get t1 = begin mathsize 12px style square root of 41 end style . 
 
hence total time taken by the ball that is thrown vertically = ( begin mathsize 12px style square root of 41 end style +1 ) s ......................(1)
Let us now calculate the time taken by the ball which is thrown downwards from building height with speed 10 m/s .
 
To find the time, we need to use "S = ut+(1/2)gt2 " , with S = 200 m, and u = 10 m/s.
 
200 = 10×t + (1/2)×10×t2    or t2 + 2×t - 40 = 0 ..............(2)
 
solving the above equation (2) for t, we get t = ( begin mathsize 12px style square root of 41 end style -1 ) s .................(3)
 
If we find the difference between the time durations given in eqn.(2) and eqn.(3), we find the difference of 2 s
 
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Instead of doing the elaborate calculation as given above, we can get the answer in an alternate way.
when the ball thrown with speed 10 m/s from top of the building, it reaches the same point during its vertical fall with speed 10m/s. 
Hence both the balls are at same speed at the building height during their vertical fall. Hence time duration to reach the ground will be same.
Only difference is, the ball which is thrown vertically travel 1 s to reach the maximum height and another 1 s to reach the top of building when it falls downwards.
Hence only this 1+1 = 2 s difference between the journey of two balls.
Answered by Thiyagarajan K | 22 Jun, 2018, 03:54: PM
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