Final answer:
To find the time when the baseball reaches its maximum height, we use the vertical velocity equation, setting it equal to zero and solving for time. Assuming the initial velocity is entirely vertical, the time at maximum height would be 2 seconds.
Step-by-step explanation:
The student's question seems to be about the maximum height a baseball reaches when hit with an initial velocity given a certain equation of motion. This question falls under the subject of kinematic equations in projectile motion, which is a part of Physics, but given the context of a schoolwork question, this is also a classic Mathematics problem typically encountered in an algebra or pre-calculus class in High School.
To find the time at which the baseball reaches its maximum height, we can use the kinematic equation that describes vertical motion under the influence of gravity. The general form of the equation for vertical motion is: y = y0 + v0yt - (1/2)gt2, where y is the final height, y0 is the initial height, v0y is the initial velocity in the vertical direction, t is the time, and g is the acceleration due to gravity (applicable in the case of Earth, approximately 32 feet per second squared).
Since the student has not provided the specific equation they were instructed to use, it's difficult to offer a precise answer. Generally, the maximum height is reached when the vertical velocity becomes zero, which is where the derivative of the position function with respect to time equals zero. In practice, we can find the time at which the ball reaches its highest point by setting the vertical velocity equation v = v0 - gt equal to zero and solving for t (v is the vertical velocity at time t, v0 is the initial vertical velocity, and g is the acceleration due to gravity). Applying this to the given initial velocity of 64 feet per second (presuming it's in the upward - vertical direction), we get: 0 = 64 - 32t, solving for t gives the time at which the ball reaches its maximum height: t = 2 seconds.