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प्रश्न
A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground?
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उत्तर
Given:
Height of the balloon from the ground, s = 60 m
Balloon is moving upwards with velocity 7 m/s.
The balloon and the ball are moving upwards with the same speed.
When the ball is dropped, its initial velocity (u) is −7 m/s.
Acceleration due to gravity, a = g = 9.8 m/s2
Using the equation of motion, we have:
\[ \Rightarrow 60 = - 7t + 4 . 9 \times t^2 \]
\[ \Rightarrow 4 . 9 t^2 - 7t - 60 = 0\]
\[t = \frac{7 \pm \sqrt{49 - 4 \times 4 . 9 \times \left( - 60 \right)}}{2 \times 4 . 9}\]
\[t = \frac{7 \pm \sqrt{\left( 49 + 1176 \right)}}{9 . 8}\]
\[t = \frac{7 \pm 35}{9 . 8}\]
Time taken by the ball to reach the ground = 4.3 s
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