1. An airplane propeller has a diameter of 2 m. At 3000 rpm, calculate the speed of the tip of the propeller and the centripetal acceleration at the tip. Express your answers in terms of (1) the sound speed in air (340 m s-1 ) and g (10 m s-2 ).
2. The same propeller speeds up from 1000 rpm to 3000 rpm in 2 seconds. a. Calculate the angular acceleration (assumed constant). b. How many revolutions does the propeller make during this time? c. Calculate the tangential acceleration at the tip and compare to the centripetal acceleration (at 3000 rpm) calculated above. What is the magnitude and direction of the total acceleration vector?
3. A cannon on a horizontal battlefield fires a ball at a speed of 30 m s-1 . The cannon is angled at 30 degrees to the horizontal. a. What are the initial components of the cannonball velocity? b. How long does it take for the ball to reach its maximum height? c. What is the maximum height reached? d. How long does it take for the cannonball to hit the ground? e. How far does it travel horizontally?
4. A baseball leaves a bat at a height of 1 m above the ground, at a speed of 50 m s -1 and an angle of 20 degrees (measured upward from the horizontal). a. How long does the ball spend in the air (i.e. above ground level)? b. Does it make it to the outfield wall (130 m distant)? If so, how long does the ball take to travel to the outfield wall? c. What altitude does the ball have at this time? Does it clear the 5 m high outfield wall for a home run?
5. A ball is thrown at a speed of 25 m s -1 at an angle of 53.1o (measured upward from the horizontal) from the top of a 25 m tall cliff. a. What are the initial components of the velocity vector? b. What is the maximum height reached by the ball, and when does it reach it? What is the distance from the release point at this time? c. What are the components of the velocity when the ball hits the ground? d. What is the ball's speed when it hits the ground? e. How far from the base of the cliff does the ball land?