Final answer:
To model the height of the ball thrown from a platform, a standard kinematic equation for vertical motion is used. The time to reach maximum height is found when vertical velocity equals zero. The ball hitting the ground is determined by solving the height equation using the quadratic formula for time when height equals zero.
Step-by-step explanation:
The question pertains to the kinematics of a projectile in a physics context, where a ball is thrown into the air from a height of 10 feet with an initial velocity of 38 us (likely meaning feet per second, considering the unit for height). To model the height of the ball as a function of time, we use the standard kinematic equation for vertical motion under gravity, which is:
y = y0 + v0t - ½gt2
Here, y is the final height, y0 is the initial height (10 feet), v0 is the initial velocity (38 ft/s), g is the acceleration due to gravity (32.2 ft/s2), and t is the time in seconds. The negative sign before the gravity term accounts for the downward acceleration of gravity.
To calculate how long it takes the ball to reach its maximum height, you set the velocity to 0 because at the maximum height, the vertical velocity is zero. From the equation v = v0 - gt, we solve for t to find the time to reach maximum height.
The ball will hit the ground when y equals 0. Using the quadratic formula to solve for t in the height equation would provide the times at which the height is 0. There will be two solutions: the time at which the ball was thrown and the time it hits the ground, and we take the positive solution for the actual impact time.
Experimentally, when conducting a ballistic motion experiment, one would typically use video analysis or motion sensors to measure the maximum height and time of flight of a projectile. The resulting data allows the experimenter to construct a time-height graph and analyze the motion. Factors like air resistance can affect the results, making the projectile's actual path differ slightly from the ideal parabolic trajectory predicted by kinematic equations.