think its a quadratic equation but not sure hence why i need help

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June 3rd 2012, 01:59 PM
gordonmckee

think its a quadratic equation but not sure hence why i need help

A ball is thrown down at 72 km h–1 speed from the top of a building. The
building is 125 metres tall. The distance travelled before it reach the
ground is as follows,

s = u0t + 1/2gtsquared

where:
u0 = initial velocity (ms -1)
g = acceleration due to gravity (10 ms -2)
t = time (s)

Find the time for the ball to drop to fifth of the height of the building.
&
Find the time for the ball to reach the ground.
June 3rd 2012, 02:54 PM
skeeter

Re: think its a quadratic equation but not sure hence why i need help

Quote:

Originally Posted by gordonmckee

A ball is thrown down at 72 km h–1 speed from the top of a building. The
building is 125 metres tall. The distance travelled before it reach the
ground is as follows,

s = u0t + 1/2gtsquared

where:
u0 = initial velocity (ms -1)
g = acceleration due to gravity (10 ms -2)
t = time (s)

Find the time for the ball to drop to fifth of the height of the building.

$\color{red}{100 = 72t + 5t^2}$

&

Find the time for the ball to reach the ground.

$\color{red}{125 = 72t + 5t^2}$

... solve each equation for t
June 4th 2012, 11:05 AM
gordonmckee

Re: think its a quadratic equation but not sure hence why i need help

need a little bit more help with that ...sorry
June 4th 2012, 11:29 AM
earboth

Re: think its a quadratic equation but not sure hence why i need help

Quote:

Originally Posted by gordonmckee

A ball is thrown down at 72 km h–1 speed from the top of a building. The
building is 125 metres tall. The distance travelled before it reach the
ground is as follows,

s = u0t + 1/2gtsquared

where:
u0 = initial velocity (ms -1)
g = acceleration due to gravity (10 ms -2)
t = time (s)

Find the time for the ball to drop to fifth of the height of the building.
&
Find the time for the ball to reach the ground.

1. Convert $u_0 = 72\ \frac{km}h = 20\ \frac ms$

2. $\frac15$ of the height is 25 m; thus the ball has travelled 100 m. Therefore you have to solve for t:

$100 = 20t + \frac12 \cdot 10\ \frac m{s^2} \cdot t^2$

3. When the ball hits the ground it has travelled 125 m; thus you have to solve for t:

$125 = 20t + \frac12 \cdot 10\ \frac m{s^2} \cdot t^2$
June 4th 2012, 11:41 AM
gordonmckee

Re: think its a quadratic equation but not sure hence why i need help

thanks but its the solving part im having trouble with
June 4th 2012, 11:52 AM
earboth

Re: think its a quadratic equation but not sure hence why i need help

Quote:

Originally Posted by gordonmckee

thanks but its the solving part im having trouble with

Use the quadratic formula:

A quadratic equation

$ax^2+bx+c=0$

has the solution:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Re-write your equation into the form above. Then plug in the values you know.

Keep in mind that a negative time is not very plausible.
June 4th 2012, 12:10 PM
gordonmckee

Re: think its a quadratic equation but not sure hence why i need help

tried it and got 2.899 or -6.899.....am I doing this right or gone wrong somewhere?
June 4th 2012, 01:58 PM
HallsofIvy

Re: think its a quadratic equation but not sure hence why i need help

That's not at all what I get. Could you show your calculations?

(Of course, the quadratic equation will have two roots but the ball is not likely to hit the ground before it was thrown upward, is it?)
June 4th 2012, 02:26 PM
gordonmckee

Re: think its a quadratic equation but not sure hence why i need help

100 = 20t + 5tsquared
a= 5
b= 20
c= -100

x= -20 +or- the sqrt (20squared -4x5x-100) / 2 x 5
= -20 + or - sqrt 2400 / 10
=-20 + or - 48.99 / 10
=2.899 or -6.899
June 4th 2012, 02:26 PM
Reckoner

Re: think its a quadratic equation but not sure hence why i need help

Quote:

Originally Posted by HallsofIvy

That's not at all what I get. Could you show your calculations?

Those do appear to be the (approximate) roots of the equation for the first problem, unless I'm missing something (maybe you didn't convert the initial velocity to m/s?). Naturally, we would discard the negative root.