Respuesta :
given h = 600 - 16t ( add 16t to both sides )
16t + h = 600 ( subtract h from both sides )
16t = 600 - h ( divide both sides by 16 )
t = [tex]\frac{600-h}{16}[/tex]
when h = 400
t = [tex]\frac{600-400}{16}[/tex] = [tex]\frac{200}{16}[/tex] = 12.5 seconds
Answer:
The required time is 3.54 seconds approximately or [tex]\frac{5}{2}\sqrt{2}[/tex] seconds.
Step-by-step explanation:
Consider the provided function.
[tex]h(t) = 600-16t^2[/tex]
Where t represents the time in seconds and h represents the height.
It is given that we need to find the time to reach a height of 400 feet.
Substitute h(t)=400 in the above function.
[tex]400= 600-16t^2[/tex]
[tex]400- 600=-16t^2[/tex]
[tex]-200=-16t^2[/tex]
[tex]200=16t^2[/tex]
[tex]\frac{50}{4}=t^2[/tex]
[tex]t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}[/tex]
Neglect the negative value as time should be a positive number.
Or
[tex]t\approx 3.54[/tex]
Hence, the required time is 3.54 seconds approximately.
