A diwali rocket moves vertically up with a constant acceleration of 8m/s2. After some time, its fuel gets exhausted and then falls freely under gravity. If maximum height attained by the rocket is 180 m then calculate the speed when the fuel is just exhausted. (g= 10m/s2)
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Solution:
⠀⠀⠀⠀⠀⠀⠀⠀⠀
Let rocket acquires a speed v at the time when fuel gets exhausted. (Then referring the v-t graph)
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
Similarly,
⠀⠀⠀⠀⠀⠀⠀⠀⠀
From above equations, we have,
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v =
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Area under (v - t) graph = Area of ∆OPQ
⠀⠀⠀⠀⠀⠀⠀⠀⠀
S =
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
Hence, speed of rocket when fuel is just exhausted will be 40 m/s.
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