Question

a canon on a hill, 50m above sealevel fires a shot with v=600m/s to a ship with distance 12000m. At which angle should the shot be fired?

Answer 1

i don't understand how i can know if the shot is fired up, horizontal or down...?

Answer 2

First check if fired horizontal can it reach there.
If it can, it is fine.
Otherwise, it has to be fired at an angle.
Can you try?

Answer 3

sure

Answer 4

Are you able to proceed?

Answer 5

need to find the right formulas

Answer 6

if fired horizontally: x=v.t and y=y-1/2gt^2 ?

Answer 7

Yeah, first find t from second equation. Then use the first. Check whether you get x=12000

Answer 8

alright

Answer 9

nope

Answer 10

t=3,19

Answer 11

impossibru

Answer 12

so i guess it's fired upwards?

Answer 13

good, it should be fired upwards. I hope you can continue now. If any help,ask.

Answer 14

thank you! i'll try completing it!

Answer 15

Welcome, be careful with the sign convention.

Answer 16

may i ask you for an answer to compare to mine?

Answer 17

Okay, can you wait? Will return soon with an answer.

Answer 18

ofcourse

Answer 19

my answer is around 19,27 degrees

Answer 20

What was the equation you got?

Answer 21

i probably calculated something wrong

Answer 22

i got : 12000=600.cosx.600.sinx.2/9.8

Answer 23

What was your approach?

Answer 24

well.. x=vi.cosx.t and y=yi + visinx - 1/2gt^2

Answer 25

solve y for t gives me : vi.sinx.2/g = t

Answer 26

i plug it into my x equation

Answer 27

The second equation should have a t multiplied to vi. sin x .

Answer 28

yes, forgot

Answer 29

so i get: x=vi.cosx.visinx.2/g

Answer 30

we have a quadratic in t there, am i correct?

Answer 31

which t?

Answer 32

here y=yi + visinx - 1/2gt^2 ?

Answer 33

i factored it out so i can get vi.sinx.2/g = t

Answer 34

because y = 0

Answer 35

Yes, it is
\[s = ut+ \frac{ 1 }{ 2 }a t^2\]
you forgot the t multiplied to u

Answer 36

?

Answer 37

yes, but i just forgot to type it. i included it into my calculations

Answer 38

what's s and u?

Answer 39

am i doing something wrong?

Answer 40

s- displacement
u-initial velocity
How did you factorize the equation?

Answer 41

\[-50 = 600t \sin x -\frac{ 1 }{2 } 10 t^2\]

Answer 42

i see what i did wrong here

Answer 43

forgot about the 50

Answer 44

and
\[600\cos x \times t = 12000\]

Answer 45

it's a quadratic equation

Answer 46

hmm

Answer 47

Substitute the t from second equation into the first.
But I got stuck in solving the equation.

Answer 48

so t=12000/600cosx in the y equation

Answer 49

Yeah. Try solving.

Answer 50

alright

Answer 51

After using calculator, and a quadratic equation in sin 2x. I got 9.66 degrees.
But not sure. I think its better to stop here,as we have the idea of solving but the equation is not good.

Answer 52

we're using the a wrong equation?

Answer 53

No, a bad equation. Looks difficult to solve. Hope there is some easier way.

Answer 54

yea, i'm way off

Answer 55

i'll just skip this question

Answer 56

thought it would be easy

Answer 57

okay. if you get a easier solution, please inform me. Solving completely is not important, the idea of how to solve matters.

Answer 58

alright, thanks!

Answer 59

You're welcome:)