Question
April shoots an arrow upward at a speed of 80 feet per second off a 25 foot platform the pathway of the arrow is shown in the equation h=16t^2+80t+25 where h is the height and t is the time in seconds what is the maximum height of the arrow
Answers
GPT 3.5
To find the maximum height of the arrow, we need to determine the vertex of the parabolic equation h=16t^2+80t+25.
The vertex of a parabola in the form y=ax^2+bx+c is given by the equation x=-b/(2a).
In this case, a=16, b=80, and c=25. Plugging these values into the formula, we get:
t = -80 / (2*16)
t = -80 / 32
t = -2.5
Now, substitute t=-2.5 back into the equation to find the maximum height:
h = 16(-2.5)^2 + 80(-2.5) + 25
h = 16(6.25) - 200 + 25
h = 100 - 200 + 25
h = -75
Therefore, the maximum height of the arrow is 75 feet.
The vertex of a parabola in the form y=ax^2+bx+c is given by the equation x=-b/(2a).
In this case, a=16, b=80, and c=25. Plugging these values into the formula, we get:
t = -80 / (2*16)
t = -80 / 32
t = -2.5
Now, substitute t=-2.5 back into the equation to find the maximum height:
h = 16(-2.5)^2 + 80(-2.5) + 25
h = 16(6.25) - 200 + 25
h = 100 - 200 + 25
h = -75
Therefore, the maximum height of the arrow is 75 feet.