Question

5. A ball is thrown from a platform. The equation h = -4.9t2 + 18t + 14 gives the ball's height, h, in meters in terms of time, t, in seconds. Part A: What was the initial velocity of the ball? Part B: From what height was the ball thrown? Part C: If we measure the height in feet, how would the function change? What would be the gravity coefficient?

Answer 1

We have the following:

`h=-4.9t^2+18t+14`

now,

This equation is divided as follows:

The quadratic part (-4.9t ^ 2) that represents the acceleration (gravity coefficient), the linear part (18t) that represents the velocity and the constant part (14) that is the initial height, therefore

Part A:

The initial velocity is 18 meters per seconds, the number that accompanies the linear term

Part B:

The initial height corresponds to 14 meters

Part C:

the equivalence between meters and feet is as follows

1 meter = 3.28 feet

Therefore the change of the function would be

`\begin{gathered} h=3.28\cdot(-4.9t^2+18t+14) \\ h=-16.072t^2+59.04+45.92 \end{gathered}`

The gravity coefficiente is -16.072 feet per square seconds