Chapter 1.4, Problem 92E

(a)

To determine

h as the function of t.

Answer to Problem 92E

The vertical line cross the graph at one points, hence, the given relation define $h$ as a function of $t$ .

Explanation of Solution

Given:

The function then it is not possible for a vertical line to cross a graph more than once else the graph is not the graph of a function

Calculation:

The graph represents the height $h$ of a projectile after $t$ seconds as shown below,

  

If a given graph is a function then it is not possible for a vertical line to cross a graph more than once else the graph is not the graph of a function.

To understand the crossing at two points means for a given input for getting two outputs or two $h$ values correspond to one $t$ value which violates the definition of function.

Now, draw random parallel line to check whether it is function or not.

  

Clearly here the vertical line cross the graph at one points, hence, the given relation define $h$ as a function of $t$ .

Conclusion:

The vertical line cross the graph at one points, hence, the given relation define $h$ as a function of $t$ .

(b)

To determine

The height of the projectile after 0.5 second and after 1.25 seconds.

Answer to Problem 92E

The height of projectile after 0.5 second and after 1.25 second is between 20 and 29.

Explanation of Solution

Given:

The function then it is not possible for a vertical line to cross a graph more than once else the graph is not the graph of a function

Calculation:

To find the height of projectile after 0.5 second and after 1.25 seconds, draw line parallel to haxis at $t=0.5\text{and}t=1.25$

  

From the above graph it is very clear that the height of projectile after 0.5 second and after 1.25 second is between 20 and 29. At t = 1.25 the height is at maximum point; after that it starts decreasing.

Conclusion:

The height of projectile after 0.5 second and after 1.25 second is between 20 and 29.

(c)

To determine

The domain of h.

Answer to Problem 92E

The domain is $\left[0,2.6\right]$

Explanation of Solution

Given:

The function then it is not possible for a vertical line to cross a graph more than once else the graph is not the graph of a function

Calculation:

The domain is the set of all $t$ values included on graph. Since the curve extends from zero to point 2.6.

Therefore the domain is $\left[0,2.6\right]$

Conclusion:

The domain is $\left[0,2.6\right]$

(d)

To determine

t as function of h.

Answer to Problem 92E

The given relation doesn’t define $t$ as a function of $h$ .

Explanation of Solution

Given:

The function then it is not possible for a vertical line to cross a graph more than once else the graph is not the graph of a function

Calculation:

Draw random line parallel t- axis

  

Clearly here the horizontal line cross the graph at two points, hence, the given relation doesn’t define $t$ as a function of $h$ .

Conclusion:

The given relation doesn’t define $t$ as a function of $h$ .