When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in ft/sec and “k” is the initial height in feet (as if you were on top of a tower or building).
To determine the height of the ball at any given time, we can use the equation S = -16t^2 + vt + k, where S represents the height, t represents the time in seconds, v represents the initial velocity, and k represents the initial height.
Let's break down the equation:
-16t^2: This term represents the effect of gravity on the ball's height. The coefficient -16 is half the acceleration due to gravity (g = 32 ft/s^2 for objects falling near the surface of the Earth). The term t^2 represents the time squared because the speed decreases quadratically as the ball rises.
vt: This term represents the effect of the initial velocity on the height. Since velocity is the derivative of displacement, multiplying v by t accounts for the distance traveled during the ascending motion of the ball.
k: This is the constant term that represents the initial height of the ball. It reflects the starting point of the ball at time t = 0.
To find the height of the ball at a specific time, substitute the time value into the equation and evaluate it. Make sure to know the values of v and k to get an accurate result.