The height of a ball thrown straight up from the ground into the air at time 't', is given by:
h=8t-10t^2
What is the time to go up and fall to ground
To find the time for the ball to go up and fall back to the ground, we need to determine the time when the height is equal to zero.
Given the equation for height:
h = 8t - 10t^2
Set h equal to zero:
0 = 8t - 10t^2
This equation is a quadratic equation in terms of t, so we can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the solutions for t.
The quadratic formula is:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -10, b = 8, and c = 0.
Plugging in the values, we have:
t = (-(8) ± √((8)^2 - 4(-10)(0))) / (2(-10))
t = (-8 ± √(64)) / (-20)
t = (-8 ± 8) / (-20)
t = -16 / -20 or t = 0 / -20
Simplifying the fractions, we have:
t = 4/5 or t = 0
Since time cannot be negative, we discard the negative solution.
Therefore, the time for the ball to go up and fall back to the ground is 4/5 units of time.