Can I get some physics help?

Question

A child in a boat throws a 5.80-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 22.8 kg and the mass of the boat is 36.6 kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest. - I got -0.914 m/s but it says it's not right

A 0.265-kg ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. What is the mass of the second ball? - I got 0.84 kg, also not right.

A 144-g baseball moving 26 m/s strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at 1.25 m/s. Determine the baseball's speed after the collision, Determine the total kinetic energy before the collision, Determine the total kinetic energy after the collision. - I got 13.7 m/s for the speed but since that is wrong, I figured that doing the rest would be wrong.

An internal explosion breaks an object, initially at rest, into two pieces: A and B. Piece A has 2.3 times the mass of piece B. The energy of 6000 J is released in the explosion. Determine the kinetic area of piece A and B. - For point A, I got 2700 J but I'm not sure how to get from there to point B.

I tried to do a lot of the problems but I kept getting the answers wrong! Please help :)

Whome · Accepted Answer

Best results occur if you follow YA rules and ask only one unrelated question per post.

1)  
conservation of momentum 
(5.80 + 22.8 + 36.6)(0.0) = 5.80(10.0) + (22.8 + 36.6)(v)
v = -0.9764...
v = -0.976 m/s

2)
conservation of momentum  and conservation of kinetic energy

conservation of momentum

0.265u + M(0) = 0.265v + M(u/2)
v = (0.265u - M(u/2)) / 0.265
v = u(1 - M/0.53)

conservation of kinetic energy
½(0.265)u² + ½M(0)² = ½(0.265)v² + ½M(u/2)²
(0.265)u²  = (0.265)v² + M(u/2)²
u²  = v² + (M/4)u²
u²(1 - M/4)  = v²

u²(1 - M/4)  = (u(1 - M/0.53))² 
u²(1 - M/4)  = u²(1 - M/0.53)² 
1 - M/4  = (1 - M/0.53)² 
1 - M/4  = 1 - M/0.265 + M²/ 0.2704
0  = M/4 - M/0.265 + M²/ 0.2704
0  = 1/4 - 1/0.265 + M/ 0.2704
M/ 0.2704 = 1/0.265 - 1/4
M = 0.952777...
M = 0.953 kg

3)

conservation of momentum

0.144(26) + 5.25(0) = 0.144(v) + 5.25(1.25)
v = -19.6 m/s
so speed is absolute value of velocity or 19.6 m/s

Kinetic energy after the collision is
½(0.144)(-19.6)² + ½5.25(1.25)² = 31.7 J

4) If 2700 J is correct for one piece, the other will have 6000 - 2700 = 3300 J

let's check...

conservation of momentum
let m be the mass of part B
initial momentum is zero

0 = 2.3mv + mV
2.3mv = -mV
V = -2.3v

conservation of energy assuming both fragments move only linearly with no rotation and negligible energy is lost to heat and noise.

6000 = ½(2.3m)v² + ½mV²
6000 = ½(2.3m)v² + ½m(-2.3v)²
12000 = 2.3mv² + 5.29mv²
12000 = 7.59mv²

mv² = 12000 / 7.59 =  1581

so

6000 = ½(2.3m)v² + ½m(-2.3v)²
6000 = ½(2.3)mv² + ½(-2.3)²mv²
6000 = ½(2.3)(1581) + ½(-2.3)²(1581)
6000 = 1818 + 4182

so I have to disagree with your solution as the kinetic energies for the two parts are

part A = 1818 J
part B = 4182 J

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billrussell42 · Answer

5.80-kg package out horizontally with a speed of 10.0 m/s
momentum is 5.8x10 = 58 kgm/s

mass of the child is 22.8 kg and the mass of the boat is 36.6 kg. 
total = 59.4 kg

momentum is conserved
58 kgm/s = 59.4 kg x V
V = 0.99 m/s

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Can I get some physics help?

2 Answers