a) The velocity of stone after 7 seconds is 1.62 m/sec.
b) The velocity of the stone after it has risen 25 m is -[tex]\sqrt{17}[/tex]
a) h(t) = 10t - 0.83[tex]t^{2}[/tex]
velocity = [tex]\frac{dh}{dt}[/tex](t) = 10 - 2*0.83*t
[tex]\frac{dh}{dt}[/tex] (7) = 10 - 2*0.83*7
= 1.62 m/sec
The stone after 7 seconds is 1.62 m/sec
b) h(t) = 25
10t - 0.83[tex]t^{2}[/tex] = 25
t = 50/83 (10 + [tex]\sqrt{17}[/tex])
[tex]\frac{dh}{dt}[/tex] = 10 - 2*0.83*(50/83)(10 + [tex]\sqrt{17}[/tex])
= 10 - (10 + [tex]\sqrt{17}[/tex])
= - [tex]\sqrt{17}[/tex] m/sec.
The stone after it has risen 25 m is - [tex]\sqrt{17}[/tex] m/sec.
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