Mark is having fun with bowling balls and clay. He drops balls from various heights and records their speed just before impact with a clay block. He then measures how far into the clay the ball went--see table.

a. Find a quadratic equation relating the speed v to depth of the indentation d of the ball into the clay.

b. If the ball is going 20 meters per second, how far into the clay should it go?

c. How fast was the ball going to make a 7.5 meter impact into the clay?

Speed:m/s Depth:m

1.3 .02

5.0 .30

9.13 1.0

10.0 1.2

12.91 2.0

15.0 2.7

20.0 ?

? 7.5