Need some help on a spring cannon problem

Homework Statement

Launch a .8 kg ball from a spring cannon in order to hit a target 25m away, the cannon fires at 45 degrees relative to the ground, what is the initial velocity necessary for the ball to make the distance. spring constant is 425 N/m.

fspring=-kx

The Attempt at a Solution

I really don't know how to get started on this.

Answers and Replies

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rock.freak667
Homework Helper
Start by finding the velocity. Assume the velocity is 'v' at an angle of 45°. How would you find the range (or how far the mass travels) of the ball? What relevant equations will you need?

vx=vcos45 vy=vsin45
distance is 25m
The problem is set up so i cant use energy to solve for the velocity
the only equation i can really think of is vf2=vi2+2ax
would i solve for the y component using a=-9.8??

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rock.freak667
Homework Helper
vx=vcos45 vy=vsin45
distance is 25m
The problem is set up so i cant use energy to solve for the velocity
the only equation i can really think of is vf2=vi2+2ax
would i solve for the y component using a=-9.8??
If you consider vertical motion, when the ball hits the ground again, the displacement will be zero. So you can get the time of flight from that in terms of v.

Horizontally it travels 25m. So 25 = ?

25m=0+vi(t) +1/2axt2
so i have t=25/vcostheta, this is where i don't know how to solve for time

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rock.freak667
Homework Helper
25m=0+vi(t) +1/2axt2
so i have t=25/vcostheta, this is where i don't know how to solve for time
You are confusing the vertical motion with horizontal motion.

Vertically when the ball reaches the 25m mark, the overall vertical displacement is zero.

So if you use s=vi-1/2gt2, what is t in terms of vi?

Horizontally, the horizontal distance is nothing but initial horizontal velocity x time.

Your horizontal distance is your range, 25m. So now you should be able to solve for vi

vertically t=vysintheta/4.9 so 25=vi- vysintheta/4.9??
I'm just really needing to figure this out as I'm on a time crunch

rock.freak667
Homework Helper
vertically t=vysintheta/4.9 so 25=vi- vysintheta/4.9??
I'm just really needing to figure this out as I'm on a time crunch
Ok you got vertically that t = visinθ/4.9. That gives you the time for the entire flight.

Now horizontally the distance the mass travels is 25m. Horizontal distance = initial horizontal velocity x t

What is your initial horizontal velocity?

vi=13.16??

rock.freak667
Homework Helper
vx=vcos45 vy=vsin45
distance is 25m
The problem is set up so i cant use energy to solve for the velocity
the only equation i can really think of is vf2=vi2+2ax
would i solve for the y component using a=-9.8??
vi=13.16??
See the part in bold, those are your initial horizontal and vertical velocities respectively.

25=.707vi x (.707vi/4.9) ??

rock.freak667
Homework Helper
25=.707vi x (.707vi/4.9) ??
Right yes, but remember that your '0.707' is really 1/√2, for a more accurate answer.

So you can now find vi.

To get the how much the spring is compressed, think of when the spring is compressed, it has elastic potential energy and as it is released, all of that is converted entirely into kinetic energy.