Question

The soccer ball is kicked from the brand with an actual vertical velocity of 19.6 m/s. Its height is modeled by the function h(t) = -4.9t² + 19.6t + k, where t is the time in seconds and k is a constant. What is the value of k?

Answer 1

The value of k in the function h(t) = -4.9t² + 19.6t + k, representing the height of a soccer ball, is 4.90.

Step-by-step explanation:

The function h(t) = -4.9t² + 19.6t + k represents the height of the soccer ball at a given time t, where k is a constant. To find the value of k, we can use the given information about the ball's velocity. At t = 0, the ball has a vertical velocity of 4.90 m/s, so we can substitute this value into the equation:

4.90 = -4.9(0)² + 19.6(0) + k

Simplifying the equation, we find:

k = 4.90

Therefore, the value of k is 4.90.