Solving Kinematics: Finding the Angle for a Cannon Shooting at 400m/s

[devanlevin]

A cannon shoots at 400m/s towards a target 400m high and 15000m away from it, what angles must the cannon be a
t?

this is a kinematics question i have for homework and just don't know where to turn to. i tried with the equations but seem to always have something missing

 

[Kurdt]

What have you tried? IF you show your work people will be in a better position to help you.

 

[devanlevin]

i have tried everything i can using

v(t)=vo+at
x(t)=Xo+Vot+0.5at^2
v^2-Vo^2=2a(delta)X
or other variations of these equations

every time i come up with 1 equation with 2 missing numbers and the i get stuck, for example, using the 1st and saying that at max height Vy0=0, i get stuck because i don't have sin(theta) or T
using the 2nd and saying that Yf=400 i still don't have sin(theta) or T
using the 2nd and saying Xf=15000 don't have cos(thetha) or t
ising the 3rd don't have V unless i say Vy at max height is 0 but then don't have delta Y

 

[Kurdt]

What you have to do is consider the x and y directions independently. This will give you 2 equations with 2 unknowns which you can then solve.

 

[devanlevin]

still don't know how to do it, what am i supposed to do, i found that ymax height=8163 x sin(theta), don't see how that helps me,

please help, i have another 4 questions of this sorty and can't continue my homework till i understand it, my next class is on monday and need to finish the work before it

 

[Kurdt]

for the x direction what is the final distance going to be? What is the equation that will describe that? For the y direction what is the final distance? What is the equation that will describe that? you will now have two equations with two unknowns (time and angle) you can rearrange one of them to get time in terms of angle which you can then put into the second equation and solve for the angle which is what you want.

 

[devanlevin]

i did that, i get , for x- t=3.75/cos(theta)
then i must put that same t into my y equation, but how do i get from cos(theta) to sin(theta)??

do you understand why i can't solve this or am i just being an idiot

 

[Kurdt]

If you write down exactly what you get it would help a lot. From there I would try and make the equation a quadratic in tan (theta). You already should have a sin/cos term and a 1/cos^2 term. You can use trig identities to get them into tan from there.

 

[tiny-tim]

i did that, i get , for x- t=3.75/cos(theta)
then i must put that same t into my y equation, but how do i get from cos(theta) to sin(theta)??

Hi devanlevin!

(Don't you mean 37.5?)

Show us your y equation.

 

[devanlevin]

for x
15000=400xcos(th)xt
t=37.5/cos(th)
cos(th)=37.5/t

for y
400=400xsin(th)xt-4.9t^2
t=81.633sin(th)
sin(th)=0.01225t

now from this how do i find theta??

 

[Kurdt]

for x
15000=400xcos(th)xt
t=37.5/cos(th)
cos(th)=37.5/t

for y
400=400xsin(th)xt-4.9t^2
t=81.633sin(th)
sin(th)=0.01225t
now from this how do i find theta??

Not sure what all the bold bit is. You want to substitute the t in your y equation for the t you got from the x equation.

 

[tiny-tim]

for x
15000=400xcos(th)xt
t=37.5/cos(th)
cos(th)=37.5/t

for y
400=400xsin(th)xt-4.9t^2
t=81.633sin(th)
sin(th)=0.01225t

now from this how do i find theta??

Hi devanlevin!

(have a theta: θ
and a squared: ²
oh … and stop using x to mean "times")

I don't know how you got the 81.633 either.

Hint: get cosθ and sinθ on the left, then square and add.

 

[devanlevin]

kurdt, the bold doesn't really matter,


my problem is that if i substitute the t i found from the X, i get an equation with sin(theta) and cos(theta) which i think i can turn into tan(?) but i also get cos^2 from the t^2 and then don't know how to bring them to a result for theta

400=400sin(th)x37.5/cos(th)-4.9x(37.5/cos(th))^2

 

[Kurdt]

You need to use some trig identities to turn the $\frac{1}{\cos^2(\theta)}$ term into tan function. The following is a list of trig identities.

http://en.wikipedia.org/wiki/List_of_trigonometric_identities