Question

A grasshopper can jump incredible distances, up to 20 times its length. The height
(in inches) of the jump above the ground of a 1-inch-long grasshopper is given
by h(x) = − 1
—20x2 + x, where x is the horizontal distance (in inches) of the jump. When
the grasshopper jumps off a rock, it lands on the ground 2 inches farther. Write a function
that models the new path of the jump.

Answer 1

Answer:

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Answer 2

Given:

The distance that can be jumped by the grasshopper = 20 X Length of grasshopper

Height (h) as a function of the horizontal distance of the jump (x) is given by:

$h (x) = -\frac{1}{20} x^2 + x$

To Find:

the function of the new path of the jump

Solution:

When the grasshopper jumps, it follows a parabolic path.

In order to land 2 inches further than the previous jump, the parabola should be shifted up. Let the shifting distance be d.

When the grasshopper lands, its height = 0

So the equation of this parabola will be:

0 = (-1/20) X 22² + 22 + d

or 0 = 24.2 + 22 + d

or 0 = -2.2 + d

or d = 2.2

Replacing the value of d in the initial equation,

$h'(x) = -\frac{1}{20} x^2 + x + 2.2$

Hence, the equation of the new path is:

h' (x) = (-1/20) x² + x + 2.2