The shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
The given equation for ball height
[tex]=6+30t-16t^{2}[/tex]
The equation for the blocker's height will be
[tex]=9+25t-16t^{2}[/tex]
But, the shot is made before two-tenths of a second or 0.2 seconds therefore modified equation for ball height is
[tex]=6+30(t-0.2)-16(t-0.2)^{2}[/tex]
Now for the shot to be blocked, the height of the shot-blocker must be greater than the height of the ball which is shot before 0.2 seconds :
[tex]9+25t-16t^{2} \geq 6+30(t-0.2)-16(t-0.2)^{2}[/tex]
[tex]9+25t-16t^{2} \geq6+30t-6-16(t^{2} -0.4t+0.04)[/tex]
[tex]9+25t-16t^{2} \geq30t-16t^{2} -6.4t+0.64[/tex]
[tex]9+25t\geq36.4t-0.64[/tex]
[tex]9.64\geq11.4t[/tex]
[tex]t \leq \dfrac{9.64}{11.4}=0.846[/tex]
Thus the shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
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