Write an equation and find how long it takes for the frog to land in the wateer?

Question

A frog leaps from a lily pad in a pond into the air with an initial vertical velocity of 20 feet per second. The height h (in feet) of the frog can be modeled by h=-16t^2+vt+s where t is the time (in seconds) the frog has been in the air, v is the initial vertical velocity (in feet per second), and s is the initial height. 

Answer 1

You're given the typical position function H=-16t²+Vt+S

 

You're also given that V=20

 

So the only thing to figure out is what is S? Well, the frog essentially leaps from the top of the water since he is on a lilly pad so his initial height is 0 since he started from the ground. 

 

Your position polynomial would be H= -16t²+20t+0

 

When the frog hits the water you would simply set H equal to 0 since he will be at the ground when this happens. 

 

So 0= -16t²+20t → 0=(-16t+20)t

 

Sowe know that we have the following:

 

t=0s

16t=20 → t=5/4s

 

Since we already know that the frog was at height 0 when he jumped the only logical answer is 5/4s for when it hits the water. 

 

Hope this helps.