The path of an object projected at a 45-degree angle with an initial velocity of 60 feet per second is given by the function h(x) = -32/((60)^2)x^2 + x, where x is the horizontal distance traveled in feet and h(x) is the object's height in feet.
Use a graphing calculator or another graphing utility to determine the height of the object when it has traveled 80 feet horizontally. Give your answer to the nearest tenth of a foot.
I would like an explanation for this one if possible. Want to understand it.
I got 136.9 feet
Tell me how I did
I assume you calculated h(80)
Yes sir I did
My math was wrong I got it now
23.1 feet
I think that's correct
To determine the height of the object when it has traveled 80 feet horizontally, you can use the given function h(x) = -32/((60)^2)x^2 + x.
1. First, substitute the value of 80 for x in the function:
h(80) = -32/((60)^2)(80)^2 + 80
Simplifying inside the parenthesis:
h(80) = -32/((60)^2)(6400) + 80
Calculating the square of 60:
h(80) = -32/(3600)(6400) + 80
Calculating the square of 80:
h(80) = -32/(3600)(6400) + 80
Calculating the product of 3600 and 6400:
h(80) = -32/23040000 + 80
Simplifying the division:
h(80) = -0.00000138888889 + 80
Adding the two values:
h(80) ≈ 79.9999986111111
2. Rounding the answer to the nearest tenth of a foot:
h(80) ≈ 80.0 (nearest tenth of a foot)
Therefore, the height of the object when it has traveled 80 feet horizontally is approximately 80.0 feet.