What are the times when a pellet reaches 25 meters above its initial height?

[DrPepper]

Homework Statement

A pellet is fired upward with an initial velocity of 25 m/s. At what times in the pellet 25 meters above its fired height

Homework Equations

S=ut+1/2at^2 I got it down to,
Displacement(s)=25m
U(initial velocity)=25 m/s
and a=acceleration due to gravity -9.81
I got 25=25t+1/2(-9.81)(t^2)
then 25=25t+-4.91t^2 and I am stumped

The Attempt at a Solution

I tried dividing both sides by 25t, leaving
1/t=-4.91t^2, but I really have no clue.
I can't use the quadratic formula and I need 2 times. Any hints would be very nice! Thank you.

 

[kiwikahuna]

I'm a little bit confused, are you not allowed to use the quadratic formula for this problem? The quadratic formula is the perfect way to solve for those two times.

 

[DrPepper]

I'm a little bit confused, are you not allowed to use the quadratic formula for this problem? The quadratic formula is the perfect way to solve for those two times.

Well I am in grade 10, and we haven't learned it yet, so it is off limits. Sorry for the confusion

 

[kiwikahuna]

In that case, you should find the final velocity of this projectile motion. After you find the final velocity, you can find the times using the definition of acceleration.

 

[Ks. Jan Jenkins]

Well, let's start with what you arrived at:

25=25t+-4.91t^2

Now just factor this equation to find the values of t. You probably know the method of completing the squares, that is :

-4.9t^2 + 25t = 25

Dividing through whatever is multiplied on the square term

-t^2 + (25/4.9)t = 25/4.9

making the squared term positive

t^2 - (25/4.9)t = -25/4.9


Half the x coefficient (-25/4.9) -> (-25/9.8) and squaring it: (625/96.04) then adding this to both sides:

t^2 - (25/4.9)t + 625/96.04 = -25/4.9 + 625/96.04

then you know:

(t - 25/9.8)^2 = (625(4.9) - 25(96.04))/(4.9)(96.04)

simplifying:

(t-25/9.8)^2 = 661.5/470.596

Thus you know that

t - 25/9.8 = +/- sqrt (661.5/470.596)

as both the negative and positive numbers make a square positive number.

and thus your answers:

t = 25/9.8 +/- sqrt (661.5/470.596)

and using your trusty calculator you know now :

t = 3.736627555 (for the +)
and
t = 1.365413261 (for the -)

 

[Ks. Jan Jenkins]

P.S. Here is a site that explains a little about completing the squares:

http://www.purplemath.com/modules/sqrquad.htm