Question

A ball is thrown into the air with an initial velocity of 22 meters per second.The quadratic function h(t)=-4.9t2+22t+5.5represents the height of the ball above the ground,in meters, with respect to time t,in seconds.

Answer 1

Question:

A ball is thrown into the air with an initial velocity of 22 meters per second.

The quadratic function h(t) = -4.9t2 + 22t + 5.5 represents the height of

the ball above the ground, in meters, with respect to time t, in seconds.

Determine h(3) and explain what it represents.

Answer:

h(3) = 27.4

h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.

Solution:

The quadratic equation that represents the height of the ball above the ground, h(t), in meters, with respect to time, t, in seconds is given by:

$h(t) = -4.9t^2+22t+5.5$

To find h(3), substitute t = 3 into given quadratic equation and solve for it

Plug in t = 3 in h(t)

$h(3) = -4.9(3)^2+22(3)+5.5\\\\\text{Simplify the above expression }\\\\h(3) = -4.9 \times 9 + 66 + 5.5\\\\h(3) = -44.1+66+5.5\\\\h(3) = 27.4$

Thus h(3) = 27.4

h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.