Velocity and Acceleration

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Presentation transcript:

Velocity and Acceleration Section 11.3 AP Calculus

Example 1 Find the velocity, speed, and acceleration of the object given by

Example 2 Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point for: (1, 1)

Example 3 Use the acceleration function to find the velocity and position vectors. Then find the position at time t = 2.

Theorem 11.3 Position Function for a Projectile Neglecting air resistance, the path of a projectile launched from an initial height h with initial speed v0 and angle of elevation θ is described by the vector function Where g is the gravitational constant (32 ft/sec2 or 9.81 m/sec2)

Example 4 Determine the maximum height and range of a projectile fired at a height of 3 feet above the ground with an initial velocity of 900 ft/sec and at an angle of 45 degrees above the horizontal.

Example 5 The quarterback of a football team releases a pass at a height of 7 feet above the playing field, and the football is caught by a receiver 30 yards directly downfield at a height of 4 feet. The pass is released at an angle of 35 degrees with the horizontal. Find the speed of the football when it is released. Find the maximum height of the football. Find the time the receiver has to reach the proper position after the quarterback releases the football.