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Calculating Angles to Solve Problems

3) A batter swings and hits a fly ball in baseball, giving it an initial velocity of 35 m/s at an angle of 40 degrees from the horizontal. The ball is impacted at 1 meter above the ground. The baseball undergoes a parabolic path that is set to just clear a 3 meter fence in center field. The center fielder, 27 meters away from the fence, on the impact of the ball, runs to the point where the ball is approaching the fence and leaps to catch the ball and prevent the homerun. Determine the minimum average speed of the outfielder (to two decimal places) that allows him to do this. Ignore air resistance and use -9.8 m/s/s for the acceleration due to gravity.

3a. Does the baseball above ever travels at its launch speed of 35 m/s after impact? Please explain fully
4) 4. A person walks into an elevator holding two masses hanging on ropes, one below the other. The top mass is 3 kg and the lower mass is 28 kg. The elevator begins to move downward with an acceleration of 4 m/s/s before reaching a constant velocity. How much is the tension in the rope (to two decimal places) between the masses during the acceleration?

4a. If the elevator cable suddenly broke and the elevator were in free fall, what would the lower hanging mass do and what would be the tension in the rope between the masses? Please explain fully.

5. A car is traveling at 69 km/hr on a flat, concrete highway. If the brakes are applied such that skidding occurs, the kinetic coefficient of friction between the road and tires is 0.8. If anti-lock brakes are properly applied then no skidding occurs and the static coefficient of friction is 1.0. Determine how much farther (to two decimal places) a skidding car would travel than a car outfitted with ABS.

5a. Would you rather skid to a stop or roll to a stop in an emergency situation? Please explain fully.
6. A hanging 2-kg block begins to accelerate a 4-kg block on a horizontal surface. But a rope connected to the wall at 60.8 degrees brings the block to an equilibrium position. What is the tension (to two decimal places) in the angled rope that is required to keep the block from accelerating? The coefficient of friction between the surface and the 4-kg block is 0.25.

6a. How does the normal force compare to the weight of the block in this problem? Please explain fully.

7. A 2-mass system is established as shown in the animation above. The 2.0-kg mass is sliding on a surface inclined at 59.5 degrees. The 2.5-kg hanging mass is allowed to drop from rest. It takes 2.1 seconds for the hanging mass to fall through 1.5 meters and hit the ground. What is the coefficient of friction (to three decimal places) between the sliding mass and the incline?

7a. If the angle of the incline above is decreased, thereby changing the normal force, what would happen to the coefficient of friction? Please explain fully.


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