Question
A ball is thrown into the air with an initial velocity of 25 meters per second. The function h(t)=-4.9t²+25t + 6 represents the height of the ball above the ground in meters, with respect to time, t, in seconds. Part A: 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 function?
Part B: the graph below represents the height of the ball with respect to time what would be a reasonable domain for the function?
Answers
Answered by
GPT 3.5
To find the height of the ball at h(3), we need to substitute t=3 into the function h(t).
h(3) = -4.9(3)^2 + 25(3) + 6
= -4.9(9) + 75 + 6
= -44.1 + 75 + 6
= 36.9 meters
So, at h(3), the height of the ball would be 36.9 meters.
For Part B, the graph represents the height of the ball with respect to time. The height of the ball can be negative if it is below the ground. However, since the question specifies the height of the ball above the ground, a reasonable domain for the function would be when the ball is in the air.
Since the ball is thrown into the air with an initial velocity of 25 m/s and will eventually reach the ground, the maximum time the ball will be in the air can be calculated using the equation h(t) = -4.9t^2 + 25t + 6 = 0 (when the ball hits the ground).
Solving the quadratic equation, we find the roots (t-values) as t = -0.183 and t = 5.374.
Therefore, a reasonable domain for the function would be from t = 0 (when the ball is thrown) to t ≈ 5.374 (when the ball hits the ground).
h(3) = -4.9(3)^2 + 25(3) + 6
= -4.9(9) + 75 + 6
= -44.1 + 75 + 6
= 36.9 meters
So, at h(3), the height of the ball would be 36.9 meters.
For Part B, the graph represents the height of the ball with respect to time. The height of the ball can be negative if it is below the ground. However, since the question specifies the height of the ball above the ground, a reasonable domain for the function would be when the ball is in the air.
Since the ball is thrown into the air with an initial velocity of 25 m/s and will eventually reach the ground, the maximum time the ball will be in the air can be calculated using the equation h(t) = -4.9t^2 + 25t + 6 = 0 (when the ball hits the ground).
Solving the quadratic equation, we find the roots (t-values) as t = -0.183 and t = 5.374.
Therefore, a reasonable domain for the function would be from t = 0 (when the ball is thrown) to t ≈ 5.374 (when the ball hits the ground).