Question

The height of an acorn from the ground, in meters, as it falls from a tree can be represented by the equation f(x) = h – 9.8x2. The acorn was 7.2 meters off the ground when it fell off the tree, and was 4.75 meters off the ground after falling for 0.5 seconds. What is the value of h?

Answer 1

h = 7.2 meters, the starting point of the acorn's journey.

Explanation:

I added the "^" to the x to make it x^2, the correct notation for this kinematic equation.

f(x) = h – 9.8x^2

where f(x) is distance travelled at time x, h is the starting height, 9.8 is m/s^2, the acceleration due to gravity, and x is time, in seconds.

We know from the problem statement that:

h = 7.2 meters from the sentence "The acorn was 7.2 meters off the ground when it fell off the tree"

This leads to

f(x) = 7.2m – 9.8x^2

For fun, we can set x = 0 (the start) and find that f(0) = 7.2 meters, as it should be.

f(0) = 7.2m – 9.8(0)^2

f(0) = 7.2 meters at x=0 (beginning height). As expected.

This should be enough to say that h= 7.2 meters. But additional information is provided, for some reason. Lets check to see that h=7.2m is still valid for this new observation.

f(x) = h – 9.8x^2

f(0.5) = 7.2m - 9.8*(0.5)^2

f(0.5) = 7.2m - 9.8*(0.25)

f(0.5) = 4.75 meters This is the actual observation, so h = 7.2 meters is correct.

4.75 = h – 9.8(0.5)^2

h = 4.75 + 9.8(0.5)^2

h = 7.2 meters