Question

The height in meters of a baseball t seconds after it is hit straight up in the air with

a velocity of 45 m/s is given by below. Will a baseball hit straight up with this
velocity hit the roof of a batting cuje with a maximum height of 64.5 m?
h=-9.8t²+45t+1.2

Answer 1

The baseball hit straight up with a velocity of 45 m/s will hit the roof of the batting cube with a maximum height of 64.5 m.

Step-by-step explanation:

To determine whether the baseball will hit the roof of the batting cube with a maximum height of 64.5 m, we need to find the maximum height of the baseball's trajectory. The height equation is given as:

h = -9.8t² + 45t + 1.2

To find the maximum height, we can use the vertex formula. The time at which the maximum height is reached is given by:

t = -b / (2a)

Using the coefficient values from the equation, we have:

a = -9.8, b = 45

Substituting these values into the equation gives:

t = -45 / (2 * -9.8) = 2.29 s

Substituting this time value back into the height equation gives:

h = -9.8 * (2.29)² + 45 * 2.29 + 1.2 = 65.2 m

Since the maximum height of the baseball is 65.2 m, which is greater than the roof height of 64.5 m, the baseball will hit the roof of the batting cube.