A ball is dropped from the top of a building. The expression #4.9x^2# gives the distance in meters the ball has fallen after #x# seconds. What is the expression that gives the distance in meters the ball has fallen after # x^2# seconds?

Question

1176 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T14:48:40

Wouldn't it be just #4.9x^4# meters?

Well, we have the distance that the ball has traveled after #x# seconds as #4.9x^2#.

In other words, we can let #x=u#, and the distance that the ball has fallen after #u# seconds is just #4.9u^2#.

That means, if we want to find the distance that the ball has traveled after #x^2#, we can let #u=x^2#.

Plugging that into the equation, we get

#d=4.9*(x^2)^2#

#=4.9x^4#