Q. 4.26 - Elementary Statistics

Question

A ball is thrown straight up in the air with an initial velocity of $64$ feet per second (ft/sec). According to the laws of physics, if you let $y$denote the velocity of the ball after $x$ seconds, $y=64-32x$.
a. Determine $b_0$ and $b_1$ for this linear equation.
b. Determine the velocity of the ball after $1, 2, 3, 4$ second.
c. Graph the linear equation $y=64-32x$, using the four points obtained in part (b).
d. Use the graph from part (c) to estimate visually the velocity of the ball after $1.5$ sec. Then calculate that velocity exactly by using the linear equation $y=64-32x$.

Step-by-Step Solution

Answer

Part(a) The value of $b_0=64$ and $b_1=-32$ for given equation.

Part(b) Velocity of ball after $1,2,3,4$ sec are $32, 0, -32, -64$ft/sec respectively.

Part(c) Required graph is given below.

Part(d) Velocity after $1.5$ sec is $16$ft/sec. Required graph is given below.

Part(a) Step 1 : Given information

We are given that a ball is thrown straight up in the air if $y$ denotes the velocity of ball after $x$ second.

Part(a) Step 2 : Simplify

Given equation is $y=64-32x$

Where 

$y=$velocity

$x=$time

$b_0=$Intercept

$b_1=$Slope

From given equation

$$\begin{gathered} b_0=64 \\ {b}_1=-32 \end{gathered}$$

Part(b) Step 1 : Given information

We are given that a ball is thrown straight up in the air if $y$ denotes the velocity of ball after $x$ second.

Part(b) Step 2 : Simplify

As given in the question $y=64-32x$

Where,

$y=$velocity

$x=$time

Now,

$$\begin{gathered} x=1 sec \\ y=64-32\left(1\right) \\ y=32 ft/sec \\ x=2 sec \\ y=64-32\left(2\right) \\ y=0 ft/sec \\ x=3 sec \\ y=64-32\left(3\right) \\ y=-32 ft/sec \\ x=4 sec \\ y=64-32\left(4\right) \\ y=-64 ft/sec \end{gathered}$$

Part(c) Step 1 : Given information

We are given that a ball is thrown straight up in the air if $y$ denotes the velocity of ball after $x$ second.

Part(c) Step 2 : Simplify

Required graph is 

Part(d) Step 1 : Given information

We are given that a ball is thrown straight up in the air if $y$ denotes the velocity of ball after $x$ second.

Part(d) Step 2 : Simplify

Required Graph is :

$$\begin{gathered} x=1.5 sec \\ y=64-32x \\ y=64-32\left(1.5\right) \\ y=16 ft/sec \end{gathered}$$