# Quadratic Equation - I don't know how to put this in a formula

## Homework Statement

Two platforms 50m in height have targets on them. An object succeeds in impacting with both of these.

S=ut + ½ at2 can be rearranged into the form:

½ at2 + ut – s =0

This is a quadratic equation. [ ax2 + bx +c =0 ]

Use this to calculate:

I. The times at which the bird impacts the pigs.
II. How far is each of these platforms from the catapult?

## The Attempt at a Solution

I don't know how to put this information into a formula? Can anyone explain please thanks!

Simon Bridge
Homework Helper
I suspect there is some information missing.

what bird?
what pigs?
the question only talks about platforms and objects.
does the object strike both targets on the same trajectory - i.e. passes through one to hit the other.

how far apart are the platforms?
what do we know about the initial velocity?

you will recognise the formula as a kinematic equation.
in ballistics, you need to separate the motion into vertical and horizontal and apply the kinematic equations to them (or plot the v-t graph for each, and use geometry).

This is the only information that was given to me, I can't make sense of this question..

this question is trying to make the point that there will be 2 times when a projectile will reach a certain height (other than the maximum height !!) one on the way up and one on the way down.
I don't know the relevance of the bird and pig but I suspect it is irrelevant.

Simon Bridge
Homework Helper
This is the only information that was given to me, I can't make sense of this question..
Then you have not been given enough information to get a unique solution. The best you can do is derive an equation by putting in what you do know:

what is the acceleration of the projectile?
which component of the initial velocity is important?
what is the distance s in the equation going to be?

How do I put the information into a formula?

Simon Bridge
Homework Helper
... here's the thing - you have to derive the formula first.

When you start out doing physics problems, everything is about finding the right formula and putting the numbers in. Maybe a little algebra to tweak things. However, as you go on, you will get situations where there is no right formula available or the possibilities are so numerous that memorizing the formulas is wasteful. You have to get used to describing physical situations in math.

You have an equation.
It was given to you at the start.
Do you understand what that equation has to do with ballistics?

3. Two platforms 50m in height have pigs on them. The bird succeeds in impacting with both of these.

S=ut + ½ at2 can be rearranged into the form:

½ at2 + ut – s =0

This is a quadratic equation. [ ax2 + bx +c =0 ]

Use this to calculate:

I. The times at which the bird impacts the pigs.
II. How far is each of these platforms from the catapult?

----

I don’t see how a quadratic equation involving time, displacement and velocity relates to position, the equation should be a parabola that describes the path of the bird. The only thing I can think of is finding time in terms of velocity and displacement;

Therefore, to solve ax2 + bx + c = 0

Use: x = -b + -sqrt b2-4ac / 2a

a = a/2
b = u
c = -s
x = t

It will come up with 0, 1 or 2 real solutions for t, which means there are significant events at those times. If there are no real solutions, there are imaginary ones which can still be useful.

t = -u + -sqrt –u2 -4 a/2 –s / a
t = -u + -sqrt u2 + 2as / a

t1 = -u + sqrt u2 + 2as / a
t2 = -u – sqrt u2 + 2as / a

Simon Bridge
Homework Helper
You still have not answered the questions in post #5.

I don’t see how a quadratic equation involving time, displacement and velocity relates to position,
Displacement is change in position.

In ballistic motion there are two components - horizontal and vertical. Together, the result is a parabolic trajectory. Which component will by a quadratic with time?

Note: if the initial velocity is magnitude v at angle A, then the horizontal speed is vcosA and the vertical speed is vsinA.

The "bird" is only accelerating in one of those directions - which is it?

You are asked for the time it takes to travel a given vertical distance to the targets.
When the bird has reached a target 50m away - what would be it's displacement?