A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80 m at two times. The time interval being 6 sec. Find u. 

Asked by Anil | 12th Jun, 2017, 09:45: AM

Expert Answer:

 
begin mathsize 12px style Given space that space
straight s space equals space 80 space straight m space
straight a space equals space straight g space equals space minus 10 space straight m divided by straight s
Using space the space equation space straight s space equals space ut space plus 1 half at squared space comma space we space have
rightwards arrow space 80 space equals space ut space plus space space 1 half space cross times space open parentheses negative 10 close parentheses space straight t squared
rightwards arrow space 80 space equals space ut space minus space 5 straight t squared
or space rightwards arrow space 5 straight t squared space minus space ut space plus space 80 space equals space 0
Solving space the space quadratic space equation comma space we space get
straight t space equals space fraction numerator straight u space plus space square root of straight u squared minus 1600 end root over denominator 10 end fraction space and space space fraction numerator straight u space minus space square root of straight u squared minus 1600 end root over denominator 10 end fraction
Now space it space is space given space that space
fraction numerator straight u space plus space square root of straight u squared minus 1600 end root over denominator 10 end fraction space minus space space fraction numerator straight u space minus space square root of straight u squared minus 1600 end root over denominator 10 end fraction space equals space 6
or space fraction numerator space square root of straight u squared minus 1600 end root over denominator 5 end fraction space equals space 6
rightwards arrow space square root of straight u squared minus 1600 end root space equals space 30
rightwards arrow space straight u squared minus 1600 space equals space 900
rightwards arrow space straight u squared space equals space 2500
rightwards arrow space straight u space equals space plus-or-minus space 50 straight m divided by straight s
Here space we space ignore space the space negative space signand space get
straight u space equals space 50 space straight m divided by straight s end style

Answered by Yashvanti Jain | 12th Jun, 2017, 10:24: AM