A) 1s
B) 2s
C) 3s
D) 4s
Correct Answer: B
Solution :
[b] Given equation is \[s=64t-16{{t}^{2}}\] \[\therefore \] On differentiating w.r.t. t, we get \[\frac{ds}{dt}=64-32t\] Put \[\frac{ds}{dt}=0\] for maximum height \[\Rightarrow 64-32t=0\] \[\Rightarrow t=2\] Now, \[\frac{{{d}^{2}}s}{d{{t}^{2}}}=-32\] At \[t=2,\frac{{{d}^{2}}s}{d{{t}^{2}}}=-32\] Since, \[{{\left( \frac{{{d}^{2}}s}{d{{t}^{2}}} \right)}_{t=2}}<0\] \[\therefore \] Required time = 2 second
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