Chapter ISG, Problem 9.8.2.1P

(a)

To determine

To find: The model of quadratic function of the motion of the soccer ball.

Answer to Problem 9.8.2.1P

  $h=-4.9t^2+10t+0.5$

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

Initial velocity, $u=10\text{ m/s}$

Initial height, $h=0.5\text{ m}$

Gravity, $g=9.8{\text{ m/s}}^2$

Model of height of ball, $h=-4.9t^2+10t+0.5$

Where, h is height of ball and t represent time of flight.

(b)

To determine

To graph: The model of quadratic function of the motion of the soccer ball.

Answer to Problem 9.8.2.1P

  $h=-4.9t^2+10t+0.5$

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

Initial velocity, $u=10\text{ m/s}$

Initial height, $h=0.5\text{ m}$

Gravity, $g=9.8{\text{ m/s}}^2$

Model of height of ball, $h=-4.9t^2+10t+0.5$

Graph the function below:-

  

(c)

To determine

To find: When ball move rapidly.

Answer to Problem 9.8.2.1P

  $t=2.09\text{ s}$

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

  

From graph when ball is moving up rapidly.

At $t=0.556\text{ s}$ graph will more rapidly grow.

When ball will land on ground. The height of ball is 0.

  $t=2.09\text{ s}$

(d)

To determine

To find: The time of ball when it is in air.

Answer to Problem 9.8.2.1P

  $t=2.09\text{ s}$

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

  

From graph when ball is moving up rapidly.

At $t=0.556\text{ s}$ graph will more rapidly grow.

When ball will land on ground. The height of ball is 0.

  $t=2.09\text{ s}$

Difference of time $t=0\text{ and }t=2.09\text{ s}$

The length of time the ball is in air is 2.09 s

(e)

To determine

To find: The time of ball when it is in air.

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

  

From graph when ball is moving up rapidly.

At $t=0.556\text{ s}$ graph will more rapidly grow.

When ball will land on ground. The height of ball is 0.

  $t=2.09\text{ s}$

Difference of time $t=0\text{ and }t=2.09\text{ s}$

The length of time the ball is in air is 2.09 s

The time in air is 2.09 s. This is time when kick ball and land on ground.

(f)

To determine

To find: The time of ball when it is at 3 m.

Answer to Problem 9.8.2.1P

  $t=0.292,1.749$

Explanation of Solution

Given: Alana kicks a soccer ball with initial velocity of 10 m/s when the ball is 0.5 meter above the ground.

  

The model of height of ball, $h=-4.9t^2+10t+0.5$

Put $h=3$

  $\begin{array}{c}3=-4.9t^2+10t+0.5\\ 4.9t^2-10t+2.5=0\\ t=0.292,1.749\end{array}$

One time show when ball is going up

Another time when moving down.

Therefore, two value of time make sense.