A ball is allowed to fall from rest from height h. If it travels 9/25th of total height in the last second of its fall then ball will hit ground will hit ground with speed
1. 45 m/s
2. 50 m/s
3. 30 m/s
4.35 m/s

Dear Student,

Please find below the solution to the asked query:

$$\begin{gathered} \text{Supose time taken by the ball to fall is} t. \\ \text{So height h is given by} h=\frac{1}{2}g{t}^2 \\ \text{and distance travelled in last second, that is t'th second is given by} \\ {h}_t=\frac{1}{2}g{t}^2-\frac{1}{2}g(t-1{)}^2 \\ \text{Now according to given problem we have} \\ \frac{1}{2}g{t}^2-\frac{1}{2}g(t-1{)}^2=\frac{9}{25}\times \frac{1}{2}g{t}^2 \\ t=5, \frac{5}{9}. \\ {\text{Now taking time t as 5 second, and g as 10 ms}}^{-2} \text{we can get the velocity } \\ \text{at which the ball hit ground is} \\ v=gt=10\times 5=50 m{s}^{-1} \\ \text{Option 2. is correct answer. } \end{gathered}$$

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