Ted popped a baseball straight up into the air at a speed of 48 ft/s. The height of the ball after t seconds is given by the function h(t) = -16t2 + 48t + 3
When does the baseball reach its maximum height?
What is the maximum height of the baseball?
When does the baseball hit the ground?
To find the maximum height of the baseball, we need to find the vertex of the quadratic function h(t) = -16t^2 + 48t + 3. The t-coordinate of the vertex is given by the formula t = -b/(2a), where a = -16 and b = 48 in this case.
So, t = -48/(2*(-16)) = -48/(-32) = 1.5 seconds.
To find the maximum height, we substitute t = 1.5 back into the function h(t):
h(1.5) = -16(1.5)^2 + 48(1.5) + 3
h(1.5) = -16(2.25) + 72 + 3
h(1.5) = -36 + 72 + 3
h(1.5) = 39 feet
Therefore, the baseball reaches its maximum height of 39 feet after 1.5 seconds.
To find when the baseball hits the ground, we need to find the time when the height is equal to 0:
0 = -16t^2 + 48t + 3
Solving this quadratic equation, we get two solutions: t ≈ 0.19 seconds and t ≈ 2.81 seconds.
Therefore, the baseball hits the ground after approximately 2.81 seconds.