Word problem question.

Question

A tree frog leaps from a branch 1 foot above a pond with an initial vertical velocity of 25 feet per second.

The height h(in feet) of the frog can be modeled by the equation h=-16x^2+25x+1

How high is the frog after 1.5 sec.?

How long will it take for the frog to reach a height of 9 feet?

What is the maximum height the frog jumps?

Answer 1

How high the frog will leap in 1.5 secs is simply putting 1.5 in for "x" in the equation h = -16x² + 25x +1. You will find that this comes out to h =10.77 ft.

How long will it take for the frog to have leaped 9 is to set the equation equal to 9 and solving for "x" :

9 = -16x² + 25x +1

0 = -16x² + 25x +1 - 9

0 = -16x² + 25x - 8

Using the Quadratic Formula, x = (-b ± √b² - 4ac)/2a, where a = -16, b = 25 and c = -8, you will find that "x" will equal .45 sec and 1.11 sec. The answer will be .45 sec because that is when the frog is going up and the 1.11 sec is when he is coming down.

The max height is at the vertex of the parabola. The "x" value for the vertex is found using x= -b/2a. Using a = -16 and b = 25 you get x = 25/32. Put this value in for "x" in the original equation and you will find that the max height is roughly 10.77 ft.

I hope this helps!