Answer:
7 meters
Step-by-step explanation:
In order to find the answer we need to calculate the first derivative of the function as follows:
[tex]h=-4.9*t^{2}+19.6*t-12.6\\h'=-4.9*2*t^{2-1}+19.6*1-0\\h'=-9.8*t+19.6[/tex]
Now, for obtaining the time 't' when the ball reaches the maximum height:
[tex]h'=0\\-9.8*t+19.6=0\\t=19.6/9.8=2[/tex]
Finally, we use the original equation for determining the height after 2 seconds:
[tex]h(2)=-4.9*2^{2}+19.6*2-12.6\\\\h(2)=7[/tex]
In conclusion, the maximum height above the cliff top is 7 meters.
The maximum height above the cliff top is 7 meters.
We have given that the equation,
[tex]h=-4.9*t^2+19.6*t-12.6[/tex]
derivative is the rate of change of a function with respect to a variable.
Here,rate of change of height and variable is time and
Therefore the derivative of given function is,
[tex]h=-4.9*t^2+19.6*t-12.6[/tex]
[tex]h'=-9.8t+19.6[/tex]
We have to find t when the ball reaches the maximum height
[tex]h'=0\\-9.8t+19.6=0[/tex]
[tex]t=\frac{19.6}{9.8}=2[/tex]
we use the original equation to find the height after 2 seconds
[tex]h(2)=-4.9*2^2+19.6*2-12.6\\h(2)=7[/tex]
Therefor we get, the maximum height above the cliff top is 7 meters.
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