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2.1) Gazelles

Gazelles are magnificent animals, native to Africa, whose ability to jump is astounding.  If a gazelle leaps at and angle of 30o above the horizontal, and travels a distance of 4 m, how long was the gazelle in the air?

2.2) Tennis Champs

Wimbledon champs Venus and Serena Williams are relaxing with a friendly tennis game.  Venus holds her tennis racket horizontally at a height of 1.5 m above the ground.  She returns an incoming ball at an angle that is 5o below the horizontal, and a speed of 10 m/s. 

If Serena runs to the ball and returns it just before it hits the ground, how much time did she have to get to the ball?  If she ran at half the speed of the ball, what is the maximum distance she could be from the ball, and still return it, assuming she can reach 0.8 m from where she stands?  With what speed would the ball hit her racket?  

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2.3) Taku Tries Tennis

Taku
Katy-Robin Garton

On a sunny afternoon you’re out playing with your dog, Taku; if you throw a tennis ball at an angle of 60 degrees above the horizontal at an initial velocity of 20 mph about how far and how fast would she have to run (in m/s) to catch the ball just before it hits the ground? Your height above ground is about 1.3 m

2.4) Break a Leg

Your friend is part of a dance company and is choreographing a modern dance that involves leaping off blocks that are placed around the stage.  She wants to know how she should place the blocks so she can get the desired aesthetic effect.  Knowing you are taking physics, she asks your advice.  Derive a general formula for your friend that gives the distance from the block that a dancer will land as a function of the height of the block (h), the initial speed of the dancer (v), and the angle that the dancer leaves the block (q).  

2.5) Diving World Cup

a) At the 1999 FINA Diving World Cup 3m competition, 22 divers did a back 2 ½ somersault in a tuck position. The remaining 6 did their back 2 ½ in the pike position. On average, those that chose to do the dive tuck left the board at an angle of 70 degrees, and were in the air for 1.3 seconds. If Wu Minxia from China does a back 2 ½ in the tuck position, with what velocity would she leave the board?

b) Jenny Keim from the United States did her back 2 ½ in the pike position. If she was also in the air for 1.3 seconds but left the board at angle of 64 degrees, what was her initial velocity?

c) How far from the diving board would Jenny and Wu hit the water?

d) What is the maximum height above the water that the Wu and Jenny reach?

e) How fast are they going when their center of mass hits the water?

**We don’t know if Jenny and WU actually did these dives at the meet.

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Kinematics Problem Set

 

Posted on 8/1/05

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