The path of a baseball after being hit is given by the function f(x)= -.007x^2+x+4 where f(x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). at what time will the baseball reach the maximum height?
To find the time at which the baseball reaches its maximum height, you need to determine the x-coordinate, or horizontal distance, at which the vertex of the parabolic function f(x) occurs. The vertex represents the maximum point of the parabola.
In this case, the given function of the baseball's path is f(x) = -0.007x^2 + x + 4. To find the x-coordinate of the vertex, you can use the formula (-b/2a), where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c. In this case, a = -0.007, b = 1, and c = 4.
Now, substitute the values into the formula: x = -b / (2a)
x = -1 / (2 * (-0.007))
x = -1 / (-0.014)
x = 71.43 feet (rounded to two decimal places).
Therefore, the baseball reaches its maximum height at a horizontal distance of approximately 71.43 feet from home plate.
no idea what time, but the distance x will be -b/2a = -1/-.014 = 71.4 ft
extra credit: given f(x) with x in feet, what is f(t), with t in seconds? recall that x(t) = v cosθ where θ is the angle of takeoff.