Answer:
Velocity = 4.33[m/s]
Explanation:
The total energy or mechanical energy is the sum of the potential energy plus the kinetic energy, as it is known the velocity and the height, we can determine the total energy.
![E_{M}=E_{p} + E_{k} \\E_{p} = potential energy [J]\\E_{k} = kinetic energy [J]\\where:\\E_{p} =m*g*h\\E_{p} = 4*9.81*0.5=19.62[J]\\E_{k}=\frac{1}{2} *m*v^{2} \\E_{k}=\frac{1}{2} *4*(3)^{2} \\E_{k}=18[J]\\Therefore\\E_{M} =18+19.62\\E_{M}=37.62[J]](https://tex.z-dn.net/?f=E_%7BM%7D%3DE_%7Bp%7D%20%20%2B%20E_%7Bk%7D%20%5C%5CE_%7Bp%7D%20%3D%20potential%20energy%20%5BJ%5D%5C%5CE_%7Bk%7D%20%3D%20kinetic%20energy%20%5BJ%5D%5C%5Cwhere%3A%5C%5CE_%7Bp%7D%20%3Dm%2Ag%2Ah%5C%5CE_%7Bp%7D%20%3D%204%2A9.81%2A0.5%3D19.62%5BJ%5D%5C%5CE_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%20%5C%5CE_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2A4%2A%283%29%5E%7B2%7D%20%5C%5CE_%7Bk%7D%3D18%5BJ%5D%5C%5CTherefore%5C%5CE_%7BM%7D%20%3D18%2B19.62%5C%5CE_%7BM%7D%3D37.62%5BJ%5D)
All this energy will become kinetic energy and we can find the velocity.
![37.62=\frac{1}{2} *m*v^{2} \\v=\sqrt{\frac{37.62*2}{4} } \\v=4.33[m/s]](https://tex.z-dn.net/?f=37.62%3D%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B37.62%2A2%7D%7B4%7D%20%7D%20%5C%5Cv%3D4.33%5Bm%2Fs%5D)
Chemical energy holds molecules together by forming the bonds between atoms. the form of electric bonds.
(a) At its maximum height, the ball's vertical velocity is 0. Recall that

Then at the maximum height
, we have


(b) The time the ball spends in the air is twice the time it takes for the ball to reach its maximum height. The ball's vertical velocity is

and at its maximum height,
so that


which would mean the ball spends a total of about 5.6 seconds in the air.
(c) The ball's horizontal position in the air is given by

so that after 5.6 seconds, it will have traversed a displacement of


Answer: 12) 1.07 m/s (right) 13) 4.05 m/s 14) 73 m/s 15) 10.9 m/s
Explanation:
12) Conservation of momentum. Momentum is the produce of mass and velocity.
13(2) + 15(-5) = 13(-5) + 15v
v = 1.06666... ≈ 1.07 m/s (right)
13) 18(9) + 22(0) = 18v + 22v
v = 18(9)/40 = 4.05 m/s
14) 0.65(35) + 0.08(0) = 0.65(26) + 0.08v
v = 73.125
15) This is a bit trickier. Let's ASSUME you jump off at 7 m/s relative to the truck. Doing this, we can assume that the reference frame is moving along with the truck at 10 m/s
the conservation of momentum equation becomes
600(0) + 80(0) = 600v + 80(-7)
v = 0.9333333... m/s
adding back the velocity of the reference frame means the truck is now traveling.
10.9333333... ≈ 10.9 m/s