What is the largest speed this projectile can have without causing the cable to break?

Question

A 20.0 wood ball hangs from a 2.10 -long wire. The maximum tension the wire can withstand without breaking is 600 . A 0.900 projectile traveling horizontally hits and embeds itself in the wood ball.

Answer 1

Once again, we have the problem of a screen shot that fails to pick up the units because they are in graphic form. You should read and correct such questions before you post them. Anyway, assuming that units are compatible, you have a resulting tangential velocity whose maximum centripetal force Fc = the breaking strength. Call the projectile speed v2. m1 and m2 are masses of block and projectile respectively. Block speed v1 = 0.
Maximum Fc = mv^2/r + gm
v = sqrt((Fc-gm)*r/m)
m = m1 + m2
From conservation of momentum,
v = m2v2/m ==>
v2 = vm/m2 (answer)