
A bomb of at rest explodes into three equal pieces, two of them found to move perpendicular to each with speed. Find the speed and the direction of piece.
Answer
148.5k+ views
Hint: Calculate the angle made by the third piece of exploded bomb. Adding and squaring in the equation to obtain the speed of the third piece of the exploded bomb.
Complete step by step answer:
Let us represent the first piece of the bomb by and represent the second piece by and represent the third piece by . And represent the speed of pieces by .
A bomb of is exploded into three equal pieces. Two of them are right angled to each. The speed of the two pieces is .
Let us consider the figure,

The linear momentum is conserved before and after the explosion of the bomb.
So, the bomb is at rest before it explodes. Therefore, zero is the initial momentum of the bomb.
We consider that the piece moves along axis, and the piece along the axis, we assume that the third piece moves towards the angle of with the negative axis at speed of
The axis is conserving,
Now we simplify the above expression.
And the axis is conserving,
Now we simplify the above expression as,
From equation (1) and (2) we get,
Now we substitute the values as,
Now, solve the above expression as,
Now, solve further for angle .
,
So, we calculate as,
Now we solve the above expression as,
The third piece moves with an angle of with .
Now, calculate the speed of the third piece and adding equation and ,
By simplifying the above relation, we get,
Now we are squaring both sides to get
Now, simplify the expression.
Now, solve the expression further.
We solve the value of as,
Therefore, the speed of the third piece that explodes is .
Note: As we know that the velocity is the vector quantity and the resultant of the velocities will be calculated by using the vector addition that is it depends on the direction of the velocities.
Complete step by step answer:
Let us represent the first piece of the bomb by
A bomb of
Let us consider the figure,

The linear momentum is conserved before and after the explosion of the bomb.
So, the bomb is at rest before it explodes. Therefore, zero is the initial momentum of the bomb.
We consider that the piece
The
Now we simplify the above expression.
And the
Now we simplify the above expression as,
From equation (1) and (2) we get,
Now we substitute the values as,
Now, solve the above expression as,
Now, solve further for angle
So, we calculate as,
Now we solve the above expression as,
The third piece moves with an angle of
Now, calculate the speed of the third piece and adding equation
By simplifying the above relation, we get,
Now we are squaring both sides to get
Now, simplify the expression.
Now, solve the expression further.
We solve the value of
Therefore, the speed of the third piece that explodes is
Note: As we know that the velocity is the vector quantity and the resultant of the velocities will be calculated by using the vector addition that is it depends on the direction of the velocities.
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
School Full course for MAHARASHTRABOARD students
₹33,300 per year
EMI starts from ₹2,775 per month
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Uniform Acceleration

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Degree of Dissociation and Its Formula With Solved Example for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry
