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Projectile Motion for an Object Launched at an Angle

Determine flight time and distance of angular projectile launches

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To Hit An Ace

To Hit An Ace

Credit: Emmett Hume
Source: http://commons.wikimedia.org/wiki/File:John_Isner_2009_US_Open.jpg
License: CC BY-NC 3.0

During the 2010 Wimbledon match between John Isner and Nicolas Mahut, Isner set the record for the most number of aces in a match at 113. An ace is considered a legal serve that is not touched by the receiver, resulting in a point for the server.

Amazing But True

  • An ace is where a point is rewarded for a legal serve that the opponent does not touch. A legal serve in tennis is one where the server hits the ball across the net into the service court on the opposite side of the center service line. The area the ball has to enter has the dimensions 6.4 \ m \times 4.11 \ m.
  • Credit: Eric Flemming
    Source: http://www.flickr.com/photos/68105231@N00/2315297041
    License: CC BY-NC 3.0

    In order to hit an ace, the tennis player must serve the ball into the legal service court without having the opponent hit it back [Figure2]


  • The speed at which the ball is hit at greatly determines the angle at which the ball must be hit at for it to pass the top of the net. This delicate balance between variables is what separates the good tennis players from the best. Use the diagram below to answer the following questions about this relationship.

License: CC BY-NC 3.0

Can You Apply It?

Using the information provided above, answer the following questions.

  1. Which of the two velocity vectors would require the server to hit the ball at a higher point from its release?
  2. Which serve is under the influence of gravity for a longer period of time before hitting the ground?

Image Attributions

  1. [1]^ Credit: Emmett Hume; Source: http://commons.wikimedia.org/wiki/File:John_Isner_2009_US_Open.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Eric Flemming; Source: http://www.flickr.com/photos/68105231@N00/2315297041; License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0

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