(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I launched a projectile from a slingshot to different distances by pulling the band back different distances. The projectile was launched horizontally, and the slingshot was a fixed height, 48 cm, above ground.

Known Data for the first run:

Height: 48 cm

Distance the band was pulled back: 4 cm

Force on the band at this stretched point: 1 N

Average distance the projectile traveled after launch: 17 cm

Mass of projectile: 100 gm

Now I need to know how to find the initial velocity of the projectile when it leaves the slingshot, so I can theoretically determine how far the projectile ought to have gone.

2. Relevant equations

s = ut + 1/2 at^{2}

Potential Energy of Spring = 1/2 kx^{2}

3. The attempt at a solution

Using the force and the extension, I determined k from Hooke's law. Then, using k and extension, I found the potential energy in the spring. Assuming all this energy got converted to kinetic energy, I equated this potential energy to 1/2 mv^{2}. Using the known mass of the projectile, I was able to calculate the velocity of the projectile at launch.

However, using the height, gravitational acceleration, and the knowledge that the initial vertical velocity was 0, I was able to calculate the time the projectile was in motion for. Then, using the initial velocity of the projectile derived earlier, and the time, I calculated the horizontal distance it should have covered ignoring air resistance. However, the values didn't work out right.

Can you tell me where I'm going wrong, or suggest your own method for calculating the velocity of a projectile after it is launched from a slingshot.

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# Homework Help: Calculating velocity in a slingshot

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