Chapter 1.8, Problem 2E

Solution

To state: A real-life situation in which the model $h=-16t^2+v_{0}t+h_0$ can be used not the model $h=-16t^2+h_0$ .

A batsman hits a ball into the air in cricket ground.

Given information:

The models are $h=-16t^2+v_{0}t+h_0$ and $h=-16t^2+h_0$ .

Explanation:

Model $h=-16t^2+h_0$ can be used when an object is dropped then its height will be represented by h which is above the ground after t seconds.

Here $h_0$ represents the initial height of the object.

Now consider the model $h=-16t^2+v_{0}t+h_0$ .

If an object is considered that is being launched or thrown then an extra term which is $v_{0}t$ must be added to the model $h=-16t^2+h_0$ to account for the initial velocity $v_{0}t$ of the object.

Now consider the example, a batsman in the cricked ground hits a ball into the air.

In this case the model $h=-16t^2+h_0$ cannot be used but the model $h=-16t^2+v_{0}t+h_0$ can be used.