requestbook
109

Step-by-step Answer
PAGE: 463SET: ExercisesPROBLEM: 109
Please look in your text book for this problem Statement

(a)

The horizontal distance that a projectile will travel in the air (ignoring air resistance) is .

Where is the initial velocity of the projectile, is the angle of elevation,

is acceleration due to gravity ( ).

Find the angle of elevation .

Consider .

Substitute , , and in .

The general solution of is , where is an integer.

.

Find the angles on the interval .

If , then .

If , then .

Therefore, the angle of elevation and .

(b)

To find the maximum distance first find the critical points.

Consider .

Differentiate the above function with respect to .

Equate to zero.

The general solution of is , where is an integer.

.

Find the angles on the interval .

If , then .

If , then .

Therefore, the solution is on the interval .

Consider .

Differentiate the above function with respect to .

Substitue in .

By the second derivative test, the maximum distance occures at . 

Consider .

Substitue , and in .

Therefore, the maximum distance that can throw the ball is .

(c)

The function is .

Substitue   and in .

.

Draw the coordinate plane.

Use a graphing utility graph the function in the interval .

Graph :

.

(d)

Graph of :

Observe the above graph :

At , the distance that can throw the ball is .

At , the distance that can throw the ball is .

The maximum distance occurs at .

The maximum distance that can throw the ball is .

(a)

The angle of elevation and .

(b)

The maximum distance that can throw the ball is .

(c)

Graph of :

(d)

Observe the above graph :

At , the distance that can throw the ball is .

At , the distance that can throw the ball is .

The maximum distance occurs at .

The maximum distance that we can throw the ball is .



TESTIMONIALS

"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!"

June Barnett

"Your site is amazing! It helped me get through Algebra."

Charles

"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful."

Dan Pease

QUESTIONS? LET US HELP.
Simply chose a support option

My status

JOIN US ON:     
mathskey.com is not affiliated with any Publisher, Book cover, Title, Author names appear for reference only