Calculating Slingshot Projectile Motion - Finding Initial Velocity

[Physics Person]

Homework Statement

"The slingshot exerts 40 N for 0.25 s. If Red bird is released 5 meters above the ground, and kills the pig, how far away is the pig?" m = 0.75 kg; angle = 45 degrees

Homework Equations

x = (initial velocity in x-direction) * (time)[/B]

The Attempt at a Solution

In order to calculate the displacement, I need to know the initial velocity in the x direction, which is not given. Therefore, I first solved for the initial total velocity by constructing a right triangle in which the height of 5 meters above the ground is one side, and the initial total velocity is the hypotenuse. I then used trigonometric functions to find the initial total velocity, which I calculated to be approximately 7 m/s. I then constructed another right triangle in which the total initial velocity was decomposed into its vertical and horizontal components, and was about to solve for the horizontal component, when I began to have doubts about whether my earlier step of finding the initial total velocity was correct. Can I construct a right triangle in which one of the sides represents height, and the hypotenuse represents velocity? Or is this not a valid thing to do, because height and velocity are two different vectors? If it is not a valid way to solve for it, is there any other way I could find the initial velocity?

 

[kuruman]

You can assume that the 40 N force of the slingshot is constant over the time interval it acts on the bird although some might say that that's a stretch (the pun is intentional). Anyway, knowing the mass of the bird and the force you can find the acceleration and the final speed of the bird at the end of the 0.25 s interval.
You are missing the vertical equation of motion which is extremely relevant to this problem.
You have not given the vertical position of the pig. Is it on the ground?

 

[gneill]

The problem statement implies that the 40 N is constant over the 2.5 s of acceleration (how this is physically possible I don't know, but it appears to be a given). The problem is, we don't (immediately) know how long the acceleration path was, so we don't know how much kinetic energy to deduct for gravitational PE influence.

If the mass of the projectile is 0.75 kg, then the force of gravity acting is 7.35 N, a goodly portion of the 40 N accelerating force, and the launch angle of 45° suggests that some portion of that will act against the acceleration of the slingshot force. My suggestion: draw a diagram of the forces acting.

 

[haruspex]

Can I construct a right triangle in which one of the sides represents height, and the hypotenuse represents velocity?

No, it is not valid to construct a representation in which different lengths represent dimensionally different physical entities.

 

[haruspex]

If the mass of the projectile is 0.75 kg, then the force of gravity acting is 7.35 N, a goodly portion of the 40 N accelerating force, and the launch angle of 45° suggests that some portion of that will act against the acceleration of the slingshot force.

Yes, this is a little tricky. If the bird were being fired up a smooth ramp at 45 degrees it would be fairly straightforward, but exactly how does it work with a slingshot? Won't the sling also be supporting the whole weight of the bird, so either the slingshot force is above 45 degrees (to get a 45 degree dispatch angle) or the launch angle (the angle when it leaves the slingshot) will be below 45 degrees?

 

[gneill]

Tricky indeed. We might inquire what level of course this question comes from to determine what level of "trickyness" needs to be taken into account. It sometimes happens that the question poser does not realize the level of complications that ensue from apparently straightforward statements.