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# Projectile Motion for an Object Launched Horizontally

## Determine flight time and distance of horizontally-launched projectiles

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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

At the 2010 Wimbledon match between John Isner and Nicolas Mahut, Isner set the record for the greatest 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

• 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 ball has to enter within the legal dimensions of 6.4 m×4.11 m\begin{align*}6.4 \ m \times 4.11 \ m\end{align*}.

Credit: Eric Flemming
Source: http://www.flickr.com/photos/68105231@N00/2315297041

Pete Sampras tossing the tennis ball in the air for his serve [Figure2]

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

#### 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 (v1orv2\begin{align*}v_1orv_2\end{align*}) is under the influence of gravity for a longer period of time before hitting the ground?

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