MATH HW

 

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.

  https://www.youtube.com/watch?v=CKOt2T70SBg 

 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 

Due after 21 hours