What should be the launch speed from the slingshot

A bit of algebra is required, get a pad of paper. First Name. Your Response. An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers.

The plane is traveling horizontally at A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge m below.

Suppose, instead, that the plane releases the. You are a member of an alpine rescue team and must get a box of supplies, with mass 3. An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers, as illustrated below in Figure Neo has two packets of flour. The ratio of the mass of flour in Packet A to the mass of flour in Packet B is Note that we are ignoring the mass of the rubber bands and pouch in this equation, which is a reasonable assumption for the cases where the projectile has a much greater mass than the combined mass of the rubber bands and pouch.

Also note that the above figure shows a linear relationship for the draw force versus draw distance. This is not necessarily the case. In reality there may be a non-linear relationship between draw force and draw distance. Nevertheless, the stored energy is still the area under the curve, which for non-linear functions can be determined using integral calculus. Other slingshot designs are certainly possible, such as the W-shaped slingshot shown in the figure below.

I first saw this design when watching the really cool JoergSprave channel on YouTube. Once more, the red dot represents the position at which the rubber bands start being pulled drawn. The force vs. A modification of the W-shaped design is shown below. In this design the rubber bands are connected at the bottom of the frame and pulled over two rollers or Teflon coated surfaces.

The roller design is commonly shown in the JoergSprave channel. This design makes it possible for the rubber bands to have initial tension at the start position of the draw, denoted by the red dot.

Furthermore, the start position of the draw can be located in the plane of the W-shaped fork, or close to it. This start position is also the approximate release position of the projectile, and given its location in the plane of the fork the projectile will be accelerated before being released over a greater distance than with the previous two designs.

The figure below illustrates the draw force F as a function of draw distance d for this slingshot. Once again, the energy stored in the rubber bands, and delivered to the projectile assuming zero energy loss , is given by the area under the curve, which is greater than the area under the curve for the previous two designs.

Rollers are commonly used in the JoergSprave designs. Rollers minimize or eliminate frictional rubbing as the rubber bands ride over them with minimal or no slipping. This is in contrast to the rubber bands riding over a rigid edge which unavoidably introduces frictional rubbing, which is a source of energy loss.

However, rollers are also a source of energy loss given that the rollers are forced to rotate at high speed as the rubber bands ride over their surface when contracting upon release. To minimize this energy loss, rollers must be used which have as little mass as possible while being strong enough during use. As an alternative to rollers one can use Teflon coated curved surfaces on the edges of the frame which the rubber bands ride over as they contract during their release.

Teflon has very low friction which means that, like rollers, it will minimize energy loss as the rubber bands ride over the edge of the frame during their release. It is difficult to say whether using Teflon or rollers is best i. It is easiest to determine this by experimenting. But how high would this take the jumper? Now that I know the starting and final velocities for the free fall phase, I can calculate the average velocity. From the definition of average velocity I can determine the change in height.

Using the value for the starting velocity and the time, I get an increase in height of The video says "over feet" and this value agrees with that. Yes, I will make a second calculation that takes into account the air resistance forcebut just hold on for now.

Determining the acceleration during the slingshot launch is a bit more difficult. Bungee cords might seem like giant springs, but they are not. Even if they were springs the force on the rider decreases as the cords become less stretched.

This means that there is a non-constant acceleration. There are two ways to approach this acceleration problem. The first is the simplestand that is to just calculate the average acceleration.

I know the starting velocity is zero and the velocity at the end of this slingshot is Using the slingshot time, I get an average acceleration of Again, this sort of agrees with the video description of "over 6 G's". The second method to calculate the acceleration makes the assumption that the bungee is actually a spring.

However, to calculate the acceleration I would need to find the distance the spring is stretched.