1. A ball is thrown vertically upwards with a speed of 10 m/s from the top of a tower 200 m height and another is thrown vertically downwards with the same speed simultaneously. The time difference between them on reaching the ground is in second) (g= 10 m/s2) 1)12 2) 6 3)2 4) 1
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Answers
Answer:
For simpler understanding let’s consider the gravity to be 10m/s^2
and the time the balls are thrown to be t-0
The total time taken by Ball-1 from t-0 to the moment it reaches ground be t-1 and Ball-2 be t-2
We need (t-1) - (t-2)
t-1
Upward phase, u = 10m/s a= -10m/s^2 v=0, time = v-u/a = -10/-10 = 1 second
Height attained during intial phase = ut + 1/2gt^2 = 10*1 + 1/2(-10)(1)^2 = 5m
Downward Phase, u = 0 height = 205 m,
==> 205m = 0 + 1/2(10)(t^2)
t= Sqrt(41)
t-1 = 6.4031+1 = 7.4031
t-2
Height traveled = 200 m, u = 10m/s
==> 200 m = 10t + 1/2(10)(t^2)
5t^2+10t-200 = 0
t^2 + 2t - 40 = 0
t= [-2(+-)Sqrt(4–(4)(1)(-40))]/2 = [-1(+-)(1/2(Sqrt(164))] = -1 (+-) 12.8062/2 = 5.4031
Difference = 7.4031–5.4031 = 2 Seconds.
Answer:
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