Applications of Parametric Equations Dr Shildneck Projectile Motion

Applications of Parametric Equations Dr. Shildneck

Projectile Motion ▪

Example 1 A missile is launched from a 50 foot platform with an initial velocity of 700 feet per second at an angle of 34 degrees to the horizontal. A) Write the parametric set that describes the path of the missile. B) Find how long the missile is in the air. C) Find how far the missile will travel before impact. D) Find when the missile will reach its maximum altitude. E) Find what the maximum altitude of the missile is.

Example 1 A missile is launched with an initial velocity of 700 feet per second at an angle of 34 degrees to the horizontal. F) Write the rectangular equation of the path of the missile. G) Graph using your calculator and verify your answers to C and E

Example 2 AJ kicks a ball straight up with an initial speed of 35 feet per second from a height of 3 feet. A) Write the parametric set that describes the motion of the ball. B) Determine how long the ball is in the air. C) Determine the maximum height of the ball.

Example 3 A plane is 300 miles due south of a control tower. One minute later the controller notices that the plane is 6 miles east and 10 miles south of its earlier position. Write a set of parametric equations that models the motion of the plane in relation to the tower.

Example 4 A fish is stuck in the bucket of a waterwheel that is 10 feet wide. If the wheel rotates at a rate of 3 revolutions per minute, write a set of parametric equations for the position of the fish in relation to the center of the wheel (from when the fish was first caught in the bucket).