Given:
The height of an object project upward is given by the polynomial
[tex]h=-16t^2+60t+90[/tex]
where t represents the time, in seconds.
We need to determine the height after t = 2.5 seconds.
Height of an object:
The height of an object after 2.5 seconds can be determined by substituting t=2.5 in the polynomial, we get;
[tex]h=-16(2.5)^2+60(2.5)+90[/tex]
Simplifying, we get;
[tex]h=-16(6.25)+60(2.5)+90[/tex]
[tex]h=-100+150+90[/tex]
[tex]h=140[/tex]
Thus, the height of an object is 140 feet.
The height of the object at a given time is required.
The height of the object at the required time is [tex]140\ \text{feet}[/tex].
The equation of motion is
[tex]h=-16t^2+60t+90[/tex]
t = Time
Now [tex]t=2.5[/tex]
Substituting the value
[tex]h=-16\times (2.5)^2+60\times 2.5+90[/tex]
[tex]\Rightarrow h=-100+150+90[/tex]
[tex]\Rightarrow h=140\ \text{feet}[/tex]
The height of the object at the required time is [tex]140\ \text{feet}[/tex].
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