Answer to Question #102922 in Classical Mechanics for Patrick Kariuki

Question #102922
A projectile of mass 56kg is moving at a constant speed of 8 m/s when it explodes into three pieces A, B and C. A(20 kg) flies along at 20 m/s along the line of flight and B(16 kg) flies at 15 m/s at 45 degrees to the line of flight in the forward direction. Find the velocity of mass C in magnitude and direction and estimate the energy supplied in the explosion.
1
Expert's answer
2020-02-14T09:32:45-0500

As per the question,

the mass of the obje ct =56kg

initial velocity of the object = 8m/sec

let before the explosion, object was moving in the x axis.

After the explodes,

mass of A=20kg

velocity of the piece A=20m/sec along the x axis

mass of the piece B=16kg

velocity of the piece B=15m/sec

B is moving at 45 with x axis.

Mass of the object c=56-20-16=20 kg

let the velocity of the c = "v"

let C is moving at an angle "\\theta" with the horizontal.

Now applying the conservation of linear momentum

"56\\times 8=20\\times20+16\\times 15 \\cos 45+20\\times v\\cos\\theta"

"488=400+120\\sqrt{2}+20v\\cos\\theta"

"v\\cos\\theta=88-120\\sqrt{2}--------(i)"

Similarly,

"20v\\sin \\theta=16\\times\\sin 45------------(ii)"

equation (ii) is dividing by equation (i)

"\\tan\\theta=\\dfrac{4\\sin 45}{5(88-120\\sqrt{2})}"

"\\tan\\theta=-0.007"

"\\theta=0.4^\\circ"

"v\\cos\\theta=88-120\\sqrt{2}"

"v\\cos\\theta=\\dfrac{88-120\\sqrt{2}}{\\cos (0.4)}=-81.70 m\/sec"

So, piece C will move along the negative x axis with the velocity -81.7 m/sec



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS