## Does the batter hit the game-winning home run?

Does the batter hit the game-winning home run?

Many of the advantages of parametric equations become obvious when applied to solving real-world problems.

Although rectangular equations in x and y give an overall picture of an object’s path, they do not reveal the position of an object at a specific time. This is where your skills in Analytical Trigonometry come in.

A common application of parametric equations is solving problems involving projectile motion.

If an object is thrown with a velocity of v feet per second at an angle of θ with the horizontal, then its flight can be modeled by,

x = (v cos θ ) t  and y = v (sin θ ) t – 16 t^2 + h

where t is in seconds and h is the object’s initial height in feet above the ground.

x is the horizontal position and y is the vertical position, and – 16 t^2 represents gravity pulling on the object.

Depending on the units involved in the problem, use g = 32 ft/ s^2 or g 9.8 m/ s^2.

Assume that the ball is hit with an initial velocity of 140 feet per second at an angle of  45°to the horizontal, making contact 3 feet above the ground.

1. Find the parametric equations to model the path of the baseball.
2. Where is the ball after 2 seconds?
3. How long is the ball in the air?
4. Is it a home run?

show work and explain your reasoning

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Connecting the dots……….Triangles

Relating Concepts :To earn credit for this assignment, you must show work and explain your reasoning.

In chapter 7 we introduced two new formulas for the area of a triangle. We can now find the area A of the triangle using one of three formulas.

1. Draw a triangle with vertices A(-5,-2), B(-3,1), and C(0,-4), and use the distance formula to find the lengths of the sides a, b, and c.

2. Then use the traditional formula ( A = 1/2 b*h) to find the area of the triangle ABC.

3. From chapter 7, find the area of triangle ABC; showing that the 3 formulas all lead to the same area.

a) First use the law of cosines to find the measure of an angle

b)Find the area of triangle ABC using Herons Formula.

c) Find the area of triangle ABC using the Law of Sines.

4)  Demonstrate how all 3 of the formulas are equivalent. = Relating Concepts

You should find that regardless of which formula you used, all three should give the same unit of measure for area.

due after 10 hours

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Connecting the dots……….Triangles

Relating Concepts :To earn credit for this assignment, you must show work and explain your reasoning.

In chapter 7 we introduced two new formulas for the area of a triangle. We can now find the area A of the triangle using one of three formulas.

1. Draw a triangle with vertices A(-5,-2), B(-3,1), and C(0,-4), and use the distance formula to find the lengths of the sides a, b, and c.

2. Then use the traditional formula ( A = 1/2 b*h) to find the area of the triangle ABC.

3. From chapter 7, find the area of triangle ABC; showing that the 3 formulas all lead to the same area.

a) First use the law of cosines to find the measure of an angle

b)Find the area of triangle ABC using Herons Formula.

c) Find the area of triangle ABC using the Law of Sines.

4)  Demonstrate how all 3 of the formulas are equivalent. = Relating Concepts

You should find that regardless of which formula you used, all three should give the same unit of measure for area.

due after 10 hours

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" 