projectile motion, unsolvable problem?

mikau · 2008-02-02 17:16:10

i have to take a course in elementary physics for my computer science curriculum. Its pretty easy and mostly stuff I've seen before. But this problem still managed to stump me

I'm convinced now that this problem was a mistake. Based on my calculations, the fish cannot reach the insect with its given firing power, and it also cannot spit a drop in such a way that it peaks directly beneath the insect.

However, i'm also having a bad math day. For some reason i'm making a lot of silly mistakes today. Don't know what it is, but that being the case, I'm not 100% sure this problem was a mistake.

The book claims the answer is 64.8 degrees. I have checked this angle, and my calculations show that the location where the arc reaches its top is neither horizontally nor vertically aligned with the bug. BUT again, i'm having a bad math day so i don't trust myself right now.

So am i going mad or does it have no solution?

JaneFairfax · 2008-02-02 18:03:18

That looks solvable to me.

Last edited by JaneFairfax (2008-02-02 18:18:02)

mikau · 2008-02-02 18:51:07

unless I'm mistaken about what those variables stand for, that gives you θ = sin^-1 ( 1.538)

Last edited by mikau (2008-02-02 18:56:19)

JaneFairfax · 2008-02-02 19:44:35

mikau · 2008-02-02 21:53:15

ah.. u = 3.56, ok

well look at the graph that produces:

you basically constructed an arc that will peak at the same height as the insect, but doesn't touch it. The insect is at around (7.2, 5.2)

I thought i had established that vertical couldn't happen either but I realize now, i only checked horizontally.

But still, the insect isn't hit!

(edit) sorry that graph link didn't work. Here's a pic.

Last edited by mikau (2008-02-02 22:05:34)

luca-deltodesco · 2008-02-02 22:10:01

if your graph is correct, can't be math to work it out then it is infact unsolvable for the given values of u,d,phi

mikau · 2008-02-02 22:15:00

i agree. unsolvable!
I'd say 'reaches the insect' is where that problem gets unclear. APPARENTLY they meant vertical height, but i never would have guessed if i didn't know it was out of range.

JaneFairfax · 2008-02-02 23:08:48

[Oh well, never mind.]

Last edited by JaneFairfax (2008-02-03 02:50:19)

luca-deltodesco · 2008-02-02 23:40:29

JaneFairfax wrote:

Luca, have you even looked at the problem yourself?

I clearly said that i hadn't i was only stating that is is unsolvable IF his graph was correct;)

JaneFairfax · 2008-02-03 03:33:46

Please forgive me for what I posted earlier. Im terribly sorry.

Let us look at the problem using the trajectory equation:

When the shot reaches the summit of its trajectory, the horizontal distance travelled will be

Then the maximum horizontal distance travelled when the shot is at its highest point will be

On the other hand:

!

Hence the fish will never hit the insect. It will have to shoot its water with greater force, or swim closer to the insect. Mikau was right. I had not dreamt that it was possible but I must now fully concede that I was totally mistaken.

mikau · 2008-02-03 06:25:33

oh come on, Jane. don't beat yourself up! I appreciate the effort. Now we know it is in fact out of range.

mikau · 2008-02-03 06:33:53

While we're on the subject, whats the easiest way to find out how to hit a target thats not level with the firing height?

I use y = x tan(θ) + g/(2u^2) x^2 sec^2 θ, and substitute tan^2 + 1 for sec^. You then have a quadratic equation involving tan θ, and you can solve. It works but its not the fastest thing in the world.

Math Is Fun Forum

#1 2008-02-02 17:16:10

projectile motion, unsolvable problem?

#2 2008-02-02 18:03:18

Re: projectile motion, unsolvable problem?

#3 2008-02-02 18:51:07

Re: projectile motion, unsolvable problem?

#4 2008-02-02 19:44:35

Re: projectile motion, unsolvable problem?

#5 2008-02-02 21:53:15

Re: projectile motion, unsolvable problem?

#6 2008-02-02 22:10:01

Re: projectile motion, unsolvable problem?

#7 2008-02-02 22:15:00

Re: projectile motion, unsolvable problem?

#8 2008-02-02 23:08:48

Re: projectile motion, unsolvable problem?

#9 2008-02-02 23:40:29

Re: projectile motion, unsolvable problem?

#10 2008-02-03 03:33:46

Re: projectile motion, unsolvable problem?

#11 2008-02-03 06:25:33

Re: projectile motion, unsolvable problem?

#12 2008-02-03 06:33:53

Re: projectile motion, unsolvable problem?

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