A 150g fircracker is thrown at 66km/h . It explodes in the air into two pieces, with a 42g piece continuing ahead at 93km/h.How much energy is gained in the explosion by the two pieces.
I know you use k=1/2mv^2
though, do you use m1v1+m2v2=(m1+m2)vf
I am getting something like 1.42 J, am i remotely close?
Use conservation of momentum to get the velocity of the other piece, which must have a mass of 108 g.
Then add up the kinetic energies of the two pieces and see how much is gained.
You will have to convert km/h to m/s and g to kg.
66 km/h = 18.3 m/s
93 km/h = 25.8 m/s
0.15*18.3 = 0.042*25.8 + 0.108*V2
0.108 V2 = 1.66 kg m/s
V2 = 15.4 m/s
Initial KE = (1/2)(0.15)(18.3)^2
= 25.2 J
Final KE(total) = (1/2)(0.042)(25.8)^2 + (1/2)(0.108)(15.4)^2 = 14.0 + 12.8 J = 26.8 J
The increase in KE is pretty close to your answer. I get 1.6 J