a ball is thrown straight up into the air with an initial velocity of 128 ft/sec, the total amount of time in seconds that it takes the object to return to the earth can be calculated by using the quadratic, 128t-16t^2=0. Determine the "flight time," t, of the ball.
I truthfully do not know this is a tricky one
To determine the flight time of the ball, we need to solve the quadratic equation 128t - 16t^2 = 0, where t represents time.
Step 1: Start with the given quadratic equation: 128t - 16t^2 = 0.
Step 2: Simplify the equation by factoring out the common factor of 16: 16t(8 - t) = 0.
Step 3: Set each factor equal to zero and solve for t separately.
a) 16t = 0
Divide both sides of the equation by 16:
t = 0
b) 8 - t = 0
Subtract 8 from both sides of the equation:
-t = -8
Divide both sides of the equation by -1 to isolate t:
t = 8
Step 4: The solutions to the quadratic equation are t = 0 and t = 8. However, in the context of this problem, t = 0 doesn't make sense because it represents the initial time when the ball was thrown, not when it returns to the earth. Therefore, we will only consider t = 8.
Step 5: The flight time of the ball is t = 8 seconds.
Therefore, the ball takes 8 seconds to return to the earth.