A ball is thrown into the air with a initial velocity of 25 meters per second.The function h(t)+-4.9t^2+25t+6 represents the height of the t in seconds. ball above the ground in meters,with respect to time.at h(3) then the height of the ball would be. Part B: The graph below represents the height of the ball with respect to time. What would be a reasonable domain for the fuction
To find the height of the ball at t=3 seconds, we plug t=3 into the function:
h(3) = -4.9(3)^2 + 25(3) + 6
Simplifying, we get:
h(3) = -4.9(9) + 75 + 6
h(3) = -44.1 + 75 + 6
h(3) = 36.9
Therefore, the height of the ball at t=3 seconds is 36.9 meters.
For the reasonable domain of the function, we need to consider the physical limitations of the situation. In this case, the ball is thrown into the air, so we only consider the time when the ball is in the air.
Since the ball is thrown into the air, it will eventually hit the ground. The height of the ball at that point would be 0. So, we can set the function equal to 0 and solve for the positive value of t:
-4.9t^2 + 25t + 6 = 0
Using the quadratic formula, we get:
t = (-25 ± sqrt(25^2 - 4(-4.9)(6))) / (2(-4.9))
Simplifying, we get:
t = -0.17 or t = 5.47
Since time cannot be negative in this context, the reasonable domain for the function would be t ≥ 0.
Therefore, a reasonable domain for the function is t ≥ 0 seconds.