A balloon starts rising from the ground with an acceleration of 2.5ms-2. After 4seconds, a stone is released from the balloon. Ifg=10m/s2, the stone will
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Answers
Given : A balloon starts rising from the ground with an acceleration of 2.5m/s². After 4 seconds, a stone is released from the balloon. g=10m/s²,
To Find : Stone will hit ground at what time
Solution:
u = 0
a = 2.5m/s²
v = u + at = 0 + 2.5*4 = 10 m/s upward
S = ut + (1/2)at² = 0 + (1/2)2.5 * 4² = 20 m
S = 20 m
u = 10 m/s
g = - 10 m/s²
S = ut + (1/2)at²
-20 = 10t + (1/2)(-10)t²
=> -20 = 10t - 5t²
=> -4 = 2t - t²
=> t² - 2t - 4 = 0
=> t = (2 ± √ 20) /2 = 1 ± √5
negative time not possible
Hence t = 1 + √5
√5 + 1 = 3.236 sec to reach ground
Form start : 4 + √5 + 1 = 5 + √5 = 7.236 sec
Total Distance covered by stone
upward t = (0 - 10)/(-10) = 1 sec
S = 10*1 - (1/2)(10)1² = 5 m
Then Down ward = 20 + 5 = 25 m
Hence total Distance covered by stone after dropping = 25 + 5 = 30 m
Velocity of stone = 10 √5 m/s downward just before hitting the the ground
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