The maximum tension the wire can withstand without breaking is 300 n . a 0.800 kg projectile traveling horizontally hits and embeds itself in the wood ball. what is the largest speed this projectile can have without causing the cable to break?

Let's investigate the case where the cable breaks.

Conservation of angular momentum can be used to find the speed.

The projectile embeds itself to the ball, so they can be treated as a combined object. The moment of inertia of the combined object is equal to the sum of the moment of inertia of both objects.

where r is the length of the cable.

After the collision, the ball and the projectile makes a circular motion because of the cable. So, the force (tension) in circular motion is

The relation between linear velocity and the angular velocity is

So,

As can be seen, the maximum velocity for the projectile without breaking the cable is , where r is the length of the cable.

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.