A ball is kicked from ground level into the air. Its height y, in feet, after x seconds can be represented by the equation y = 40x -16x^2. What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches grond level again?
Is the answer - 25 s
ground level is y=0
0=40x-16x^2= x(40-16x)
x=0, x= 40/16=2.5seconds
To find the total elapsed time from the time the ball is kicked until it reaches ground level again, we need to determine the time when the height y is equal to zero.
Given the equation y = 40x - 16x^2, we set y equal to zero since we want to find when the height is zero:
0 = 40x - 16x^2
Next, we can factor out an x from the equation:
0 = x(40 - 16x)
To find the values of x that satisfy this equation, we set each factor equal to zero:
x = 0 or 40 - 16x = 0
From the first factor, we can see that x = 0 represents the initial time when the ball is kicked.
Solving the second factor for x, we have:
40 - 16x = 0
16x = 40
x = 40/16
x = 2.5
So, the time it takes for the ball to reach ground level is 2.5 seconds after it was kicked.
To find the total elapsed time, we sum the initial time when the ball was kicked (0 seconds) and the time it takes for the ball to reach ground level (2.5 seconds):
Total elapsed time = 0 seconds + 2.5 seconds = 2.5 seconds
Therefore, the correct answer is 2.5 seconds, not -25 seconds.