A baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square.

1. A rocket launches vertically, 5 miles away from a tracking device at the same elevation as the launch site. The tracking device measures the angle of elevation of the rocket above ground. If the angle of elevation changes at /90 radians/second, find the velocity of the rocket in miles per hour when the angle of elevation is /6 radians. A 15 foot ladder is resting against the wall.  The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of  ft/sec.  How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?

2. The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 93 square centimeters? A police officer is parked a distance from a long straight highway where the speed limit is 65 mph. The officer points the radar gun at a car that is quickly approaching. The radar gun reads the distance as 45 yards. A tenth of a second later, the radar gun again reads the distance between the officer and the car, this time as 55 yards. . Is the driver speeding, and if so by how much?

3. A baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square. If a pitcher throws a baseball at 100 miles per hour, how fast is the distance between the ball and first base changing as the ball crosses home plate? Two people are 50 feet apart.  One of them starts walking north at a rate so that the angle between them is changing at a constant rate of 0.01 rad/min.  At what rate is distance between the two people changing when = radians?

4. A ladder 55 feet tall is place against a tall building. The bottom of the ladder is sliding away from the building horizontally at a rate of 8 feet/sec. Find the rate at which the angle, between the top of the ladder and the wall is changing when the angle is 25. Express your answer in radians per sec. A kite 100 ft above the ground moves horizontally at a speed of8 ft/s. At what rate is the angle between the string attached to the kite and the horizontal decreasing when 200 ft of string have been let out?

5. Bugs and Daffy finished their final act on the Bugs and Daffy Show by dancing off the stage with a spotlight covering their every move. If they are moving off the stage along a straight path at a speed of 4 ft/s, and the spotlight is 20 ft away from this path, what rate is the spotlight rotating when they are 15 feet from the point on the path closest to the spotlight? The area of a right triangle is increasing at a rate 2 centimeters squared per second and the base is increasing at a rate of 1 centimeter per second when the base is 5 centimeters and the height is 4 centimeters, What is the rate of change of the height?.

6. A person flying a kite holds the string 5 feet above the ground level, and the string is paid out at a rate of 2 ft/sec as the kite moves horizontally at an altitude of 105 feet. Assuming there is no sag in the string, find the rate at which the kite is moving when 125 feet of string has been paid out. The length of the hypotenuse of a right triangle is 10 cm. One of the acute angles is decreasing at a rate of 5 degrees/s. How fast is the area decreasing when this angle is 30 degrees?

7. A ladder 55 feet tall is place against a tall building. The bottom of the ladder is sliding away from the building horizontally at a rate of 8 feet/sec. Find the rate at which the angle, between the top of the ladder and the wall is changing when the angle is 25. Express your answer in radians per sec. A kite 100 ft above the ground moves horizontally at a speed of8 ft/s. At what rate is the angle between the string attached to the kite and the horizontal decreasing when 200 ft of string have been let out? Bugs and Daffy finished their final act on the Bugs and Daffy Show by dancing off the stage with a spotlight covering their every move. If they are moving off the stage along a straight path at a speed of 4 ft/s, and the spotlight is 20 ft away from this path, what rate is the spotlight rotating when they are 15 feet from the point on the path closest to the spotlight? The area of a right triangle is increasing at a rate 2 centimeters squared per second and the base is increasing at a rate of 1 centimeter per second when the base is 5 centimeters and the height is 4 centimeters, What is the rate of change of the height?. A person flying a kite holds the string 5 feet above the ground level, and the string is paid out at a rate of 2 ft/sec as the kite moves horizontally at an altitude of 105 feet. Assuming there is no sag in the string, find the rate at which the kite is moving when 125 feet of string has been paid out. The length of the hypotenuse of a right triangle is 10 cm. One of the acute angles is decreasing at a rate of 5 degrees/s. How fast is the area decreasing when this angle is 30 degrees?

8. A rocket launches vertically, 5 miles away from a tracking device at the same elevation as the launch site. The tracking device measures the angle of elevation of the rocket above ground. If the angle of elevation changes at /90 radians/second, find the velocity of the rocket in miles per hour when the angle of elevation is /6 radians. A 15 foot ladder is resting against the wall.  The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of  ft/sec.  How fast is the top of the ladder moving up the wall 12 seconds after we start pushing? The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 93 square centimeters? A police officer is parked a distance from a long straight highway where the speed limit is 65 mph. The officer points the radar gun at a car that is quickly approaching. The radar gun reads the distance as 45 yards. A tenth of a second later, the radar gun again reads the distance between the officer and the car, this time as 55 yards. . Is the driver speeding, and if so by how much? Two people are 50 feet apart.  One of them starts walking north at a rate so that the angle between them is changing at a constant rate of 0.01 rad/min.  At what rate is distance between the two people changing when = radians? A baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square. If a pitcher throws a baseball at 100 miles per hour, how fast is the distance between the ball and first base changing as the ball crosses home plate?

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