A body, initial at rest, explodes into two fragments of masses M and 3M having total kinetic energy E. The kinetic energy of the fragment of mass M after the explosion is........ ​

1. A body, initial at rest, explodes into two fragments of masses M and 3M having total kinetic energy E. The kinetic energy of the fragment of mass M after the explosion is........ ​

The explosion from rest is categorised as inelastic collision. Kinetic energy of the fragment of mass M after the explosion is 3E.

Penjelasan dan langkah-langkah:

Assumption:

Assume m₁ and m₂ move in opposite direction after the explosion so that v₁ is positive and v₂ is negative. Initial velocity is zero (at rest), final velocity m₁ is v₁ and final velocity of m₂ is -v₂.

Use inelastic collision formula
Inelastic collision formula:
(m₁+m₂)V = m₁v₁ + m₂(-v₂)
(3M+M)(0) = 3Mv₁ + M(-v₂)
3Mv₁ = Mv₂
v₂ = 3v₁        ...................(1)Kinetic energy m₁ from the question
Kinetic energy m₁:
[tex]KE = \frac{1}{2}m_{1} v_{1}^{2}[/tex]
[tex]E = \frac{1}{2}(3M)v_{1}^{2}[/tex]
[tex]E = \frac{3}{2}Mv_{1}^{2}[/tex]    ..................(2)

Kinetic energy m₂:
[tex]KE = \frac{1}{2}m_{2} v_{2}^{2}[/tex]Subtitute (1)
[tex]KE = \frac{1}{2}(M)(3v_{1})^{2}[/tex]
[tex]KE = \frac{9}{2}Mv_{1}^{2}[/tex]
[tex]KE = 3(\frac{3}{2}Mv_{1}^{2})[/tex]Subtitute (2)
[tex]KE = 3E[/tex]

The kinetic energy of the fragment of mass M after the explosion is 3E. ​

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2. Simon bought 17 kg of meat. He cut the meat into 6 pieces of the same mass.Find the mass of each piece of meat correct to 2 decimal places.​

the answer is 2,83 kg per pieces

correct me if i wrong. hopefully help u

3. 7Simon bought 17 kg of meat. He cut the meat into 6 pieces of the same mass.Find the mass of each piece of meat correct to 2 decimal places.​

Penjelasan:

Simon bought 17 kg of meat, and then he cut into 6 pieces, it's mean 17 kg : 6 = 2,83 kg

4. 1. A bag of grapes has a mass of 4.55 kg. A bag of mangoes has a mass of 6.90 kg. What is the total mass of the two bags of fruits? *

Jawaban:

4.55 + 6.90 = 11.45

Penjelasan:

sorry if it's wrong, hope it helps^^

Jawaban:

4,55 + 6,90 = 11,45

Penjelasan:

total mass of the two bags of fruits is 11,45 kg

5. a laptop jas a mass 2 kg James carries 7 such laptops into the computer lab what is the total mass of the laptop?​

Jawab:

14 kg

Penjelasan dengan langkah-langkah:

1 laptop = 2 kg

7 laptop = 7 x 2 = 14 kg

6. 23.A watermelon has a mass of 12.78 kg. Its mass is thrice the mass of a papaya. Find thetotal mass of the two fruits.​

Jawaban:

mtk atau b inggris sih:)

7. a tin contains three types of cookies. The mass of Type A cookies is 1 2/9 kg. The mass of Type B cookies is 2 5/6 kg. The total mass of the three types of cookies is 5 kg. What is the mass of Type C cookies? (5 marks

Penjelasan dengan langkah-langkah:

the mass of type C cookies

= 5 kg - 1 ²/9 kg - 2 ⁵/6 kg

= 5 kg - ¹¹/9 kg - ¹⁷/6 kg

= ¹⁸⁰/36 kg - ⁴⁴/36 kg - ¹⁰²/36 kg

= ³⁴/36 kg

= ¹⁷/18 kg

8. The average mass of 9 sheep is 35 kg. The average mass of 9 sheep and 1cow is 64 kg. What is the mass of the cow? (Bukan di translate ye)

rata rata massa 9 domba = 35 kg

rata rata massa 9 domba + 1 sapi = 64 kg

berapa massa sapi?

64 - 35 = 29 kg

9. A metal bar of mass 3.6kg is cut into two pieces in the ratio 3:5. The length of the shorter piece is 45cm. Finda)the length of the longer piece. b)the length of the original metal. bar c)the mass per unit length of the bar in kg/md)the mass of the shorter piece.

The Ratio of length is 3 : 5
The length of the shorter piece = 45 cm

a) The length of the longer piece (x = ?)
[tex] \frac{3}{5}= \frac{45}{x} \\ \\ 3x = 45 \times 5 \\3x=225 \\ \\ x= \frac{225}{3} \\ \\ x= 75\ cm [/tex]

b) The length of the original is  
= 45 cm + 75 cm
= 120 cm or 1,2 m

c) The mass per meter is
= 3,6 kg / 1,2 m
= 3 kg/m

d) The mass of the shorter piece
= 3 kg/m × 0,45 m
= 1,35 kg

10. a tin contains three types of cookies. The mass of Type A cookies is 1 2/9 kg. The mass of Type B cookies is 2 5/6 kg. The total mass of the three types of cookies is 5 kg. What is the mass of Type C cookies?

Penjelasan dengan langkah-langkah:

satu kaleng berisi tiga jenis kue. Massa cookie Tipe A adalah 1 2/9 kg. Massa kue Tipe B adalah 2 5/6 kg. Massa total ketiga jenis cookies tersebut adalah 5 kg. Berapa massa cookie Tipe C?

5 - ( 1 2/9 + 2 5/6)

5 - (11/9 + 17/6)

5 - (22/18 + 51/18)

5 - 73/18

5/1 - 73/18

90/18 - 73/18

17/18

11. A bag of grapes has a mass of 4.55 kg. A bag of mangoes has a mass of16.90 kg. What is the total mass of the two bags of fruits?​

Jawaban:

total mass = grapes mass + mangoes mass

total mass = 4.55 kg + 6.90 kg

total mass = 11.45 kg

12. an empty box has a mass of 75 g. David packs 12 jars of jam, each mass 380 g into the box. What is the total mass of 9 such boxes of jam ?

Jawaban:

1 box = 12 jars of jam

the mass of 1 box of jam = 75g + (12 × 380g)

= 75g + 4.560g

= 4.635g

total mass = 9 × 4.635g

= 41.715g

Jawab:

the process:

380 x 9 = 3. 420

3. 420 + 75 = 3. 495

sorry klo salah :))

Penjelasan dengan langkah-langkah:

13. The average mass of 2 chairs is 12 kg. The mass of one of the chairs is 9 kg. What is the mass of the other chair?

Jawaban:

15kg

Penjelasan dengan langkah-langkah:

[tex]12 = \frac{9 + x}{2} \\ 9 + x = 12 \times 2 \\ 9 + x = 24 \\ x = 24 - 9 \\ x = 15[/tex]

Semogamembantu!

Jawaban:

the mass of the other chair is 15 Kg

Penjelasan dengan langkah-langkah:

Diketahui : average (rata-rata) mass of 2 chair 12 Kg

The mass of one of the chairs is 9 Kg

the mass of the other chair = x

[tex] \frac{9 + x}{2} = 12 \\ x = 15[/tex]

14. 5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the piece of metal?

Jawaban:

5/9 sepotong logam memiliki massa 7 kg. Berapa massa 2/7 dari potongan logam?

Penjelasan dengan langkah-langkah:

maap banget klo salah atau gx tepat.

15. Jerry had 1/3 of a cake. He cut it into pieces equally. Each piece was 1/9 of the whole cake. How manypieces did he cut the cake into?​

Jawaban:

3

1/3 : 3 =1/9

semoga bener

16. The average mass of 9 sheep is 35 kg. The average mass of 9 sheep and 1cow is 64 kg. What is the mass of the cow?

Jawaban:

The mass of the cow is 325kg

Penjelasan:

TobeKnown:

9 sheep = 35 kg

9 sheep + 1 cow = 64 kg

TobeAsked:

mass of the cow = . . . . ?

Solving:

as 9 sheep + 1 cow is 64 kg, so that the total average mass of those 10 animals = 64 kg

total average = [tex]\frac {(9 × 35) + (cow)}{10}[/tex] = 64

(315) + (cow) = 64 × 10

315 + cow = 640

cow = 640 - 315

cow = 325 kg

17. The total mass of a basket and a rock melon was 3.78 kg. When a pomelo was added into the basket, the total mass became 5.42 kg. The mass of the rock melon was twice the mass of the pomelo. What was the mass of the rock melon?

5.42-3.78=1.64
1.64×2=3.28so the mass of the rock melon was 3.28
[tex] \textit{Basket and Melon} = 3,78 \, kg [/tex]
[tex] \textit{Basket, Melon, Pomelo} = 5,42 \, kg [/tex]
[tex] \textit{Melon} = 2 \textit{Pomelo} [/tex]

[tex] \textit{Basket, Melon, Pomelo} - \textit{Basket and Melon} = 5,42 - 3,78 [/tex]
[tex] \textit{Pomelo} = 1,64 \, kg [/tex]
[tex] \textit{Melon} = 3,28 \, kg [/tex]

18. The mass of flour in a tin is 5/6 kg. It is packed into packets each containing 2/9 kg of flour. a. How many packets has the floor been packed into? b. What is the mass of flour remaining?

a.5/6:2/9=5/6 x 9/2=15/4=3 3/4
three packets
b.remain=3/4 kg

19. The mass of a dictionary is 1.28 kg. The mass of the dictionary is twice the mass of a storybook. The mass of an encyclopaedia is 1.4 kg more than storybook. What is the mass of the encyclopaedia?

Jawaban:

2.04 kg

Penjelasan dengan langkah-langkah:

Jika berat sebuah kamus 2 kali berat buku cerita, maka berat buku cerita adalah setengah dari berat kamus. Sehingga berat ensiklopedia adalah

1.4 kg + (1.28 ÷ 2) kg

= 1.4 kg + 0.64kg

= 2.04 kg

20. Mrs. Andin has 5 kg of flour and 9 kg of rice. The ratio of the mass of flour to the mass of rice is.....a. 5 : 9b. 9 : 5c. 2 : 3d. 3 : 2​

Jawaban:

a. 5 : 9

Penjelasan dengan langkah-langkah:

perbandingan rice 5kg 9kg