a ball is thrown upward. what is the intial vertical speed? the accleration of gravity is 9.8m/s^2 and max height is 6.5m. neglect air resistance

Guest Sep 16, 2014

#3**+8 **

I think I'd just use v^{2} = u^{2} + 2as where v = final velocity (= 0), a = gravitational acceleration (-9.8m/s^{2}), s = distance (= 6.5m)

0 = u^{2} - 2*9.8*6.5

$${\mathtt{u}} = {\sqrt{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{9.8}}{\mathtt{\,\times\,}}{\mathtt{6.5}}}} \Rightarrow {\mathtt{u}} = {\mathtt{11.287\: \!160\: \!847\: \!617\: \!969\: \!5}}$$

initial velocity ≈ 11.3 m/s

Alan
Sep 16, 2014

#1**+5 **

Hi there!

Let me help you out here.

There are two formula's you need here.

At the start, the ball only has kinetic energy (speed).

This kinetic energy can be calculated as

$$E_k = \frac{1}{2}mv^2$$

where Ek is the kinetic energy, m is the mass and v is the speed.

At 6.5 meters all the kinetic energy has transformed into potential energy (since we neglect air resistance) which has the following formula;

$$E_p = mgh$$

Where Ep is the potential energy, m is the mass, g is acceleration of gravity and h the height.

Therefore if we equate $$E_p = E_k$$

We have

$$\frac{1}{2}mv^2 = mgh$$

Which we van rewrite to

$$\begin{array}{lcl}

\frac{1}{2}v^2 = gh \mbox{ (divide both sides by m)}\\

v^2 = 2gh\\

v = \sqrt{2gh}\\

\mbox{ fill in g = 9.8 and h = 6.5}\\

v = \sqrt{2*9.8*6.5} \approx 11m/s

\end{array}$$

So the speed at the start was approximately 11 meters per second.

Reinout

reinout-g
Sep 16, 2014

#2**+8 **

Ok I might do it by calculus

$$\\\ddot y=-9.8\\

\dot y=-9.8t+v\\

y=-4.9t^2+vt\\

\mbox{max height when }\doty=0\qquad(y=6.5m)\\

-9.8t+v=0\\

v=9.8t\\\\

y=-4.9t^2+vt\\

6.5=-4.9t^2+9.8t^2\\

4.9t^2-6.5=0\\

t=\sqrt{\frac{6.5}{4.9}}\\\\

\mbox{Initial Velocity}=9.8\times\sqrt{\frac{6.5}{4.9}}=11.287\;\;m/s\\\\$$

Melody
Sep 16, 2014

#3**+8 **

Best Answer

I think I'd just use v^{2} = u^{2} + 2as where v = final velocity (= 0), a = gravitational acceleration (-9.8m/s^{2}), s = distance (= 6.5m)

0 = u^{2} - 2*9.8*6.5

$${\mathtt{u}} = {\sqrt{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{9.8}}{\mathtt{\,\times\,}}{\mathtt{6.5}}}} \Rightarrow {\mathtt{u}} = {\mathtt{11.287\: \!160\: \!847\: \!617\: \!969\: \!5}}$$

initial velocity ≈ 11.3 m/s

Alan
Sep 16, 2014

#4**0 **

I'm not sure whether this is an English expression, but in Dutch we have the expression;

'there are several ways that lead to Rome'.

I think that it pretty much sums up these answers.

I didn't know the equation Alan used.

Melody's approach is one I hadn't directly thought of, but I think I like it better than sticking your nose into physics formulas

reinout-g
Sep 16, 2014

#5**0 **

In NSW, Australia schools.

If you are doing physics you have to use the physics formulas.

If you are doing mathematics you have to use calculus.

I think that our expression is "All roads lead to Rome".

Melody
Sep 16, 2014

#6**0 **

In English the phrase is "All roads lead to Rome".

There is another (rather unpleasant) phrase: "There is more than one way to skin a cat"

The kinematics equation I used is derived directly from calculus - see my last post at http://web2.0calc.com/questions/two-students-on-a-balcony-18-8m-above-the-street-one-student-throws-a-ball-vertically-downward-13-1-m-s-at-the-same-instant-the-onther-st_1#r6

Alan
Sep 16, 2014

#7**0 **

Ai, that sounds awefully unpleasant.

Please don't skin the cat!

Several of our expressions sound very strange when you literally translate them such as;

it is a truth as a cow!

or

I can do this with two finger up my nose

or

That's as correct as a bus

So given 'all craziness on a stick' are there more english expressions that are funny or strange?

reinout-g
Sep 16, 2014

#8**+3 **

I think the "skin a cat" expression probably has more to do with the "cat-o-nine-tails" (a whip used to keep recalcitrant sailors in order in days of yore) than cute furry animals!

I must be mad, but I really like the expression "I can do this with two fingers up my nose". From now on I shall use it whenever I can!!

Alan
Sep 16, 2014