Question

An exploding cannonball is initially launched at a speed of 75.0 m/s at an angle of...

An exploding cannonball is initially launched at a speed of 75.0 m/s at an angle of 30.0 ◦ above the horizontal. At its highest point, the cannonball explodes into three pieces. The first piece, with a mass of 2.00 kg, heads straight upward at a speed of 15.0 m/s immediately after the explosion. The second piece, with mass of 2.50 kg, initially moves in the direction 15.0 ◦ above the horizontal immediately after the explosion. The third piece, with a mass of 3.00 kg, initially moves in the direction 15.0 ◦ below the horizontal immediately after the explosion. (a) How fast do the second and third pieces move immediately after the explosion? (b) How much did the energy of the system increase during the explosion?

Homework Answers

Answer #1

Speed at the highest point,

v= v0x = 75 cos30 = 65 m/s


Applying momentum conservation for the explosion,

pi = pf

(2 + 2.50 + 3) (65) i = (2 x 15 j) + (2.50 x v2 (cos15i + sin15j)) + (3 x v3 (cos15i - sin15j))

30 + 2.50 v2 sin15 - 3 v3 sin15 = 0

- 0.647 v2 + 0.776 v3 = 30 ...... (i)

487.5 = 2.415 v2 + 2.90 v3 ..... (ii)


Solving . v2 = 77.7 m/s

v3 = 103.4 m/s


(C) Ki = (2 + 2.50 + 3)(65^2)/2 = 15843.75 J  

Kf = (2 x 15^2 / 2) + (2.50 x 77.7^2 / 2) + (3 x 103.4^2 / 2)

KF = 23809 J  


Energy increase = KF - Ki = 7965 J

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A 204-kg projectile, fired with a speed of 131 m/sat a 65.0 ∘  angle, breaks into three...
A 204-kg projectile, fired with a speed of 131 m/sat a 65.0 ∘  angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally. A. Determine the magnitude of the velocity of the third fragment immediately after the explosion. B....
An object of mass m, initially moving at 3.7 along the x-axis, explodes into two pieces....
An object of mass m, initially moving at 3.7 along the x-axis, explodes into two pieces. The first piece, 85 percent of the mass, moves along the negative x-axis at 6.43 m/s. Find the speed, in m/s, of the other piece right after the explosion.
Two blocks slide on a collision course across a frictionless surface, as in the figure. The...
Two blocks slide on a collision course across a frictionless surface, as in the figure. The resulting collision is inelastic. The first block has mass ,M = 1.40 kg and is initially sliding due north at a speed of Vi = 9.15 m/s. The second block has mass ,m = 7.20 ✕ 10−2 kg and is initially sliding at a speed of  vi = 11.5 m/s directed at an angle θ = 27.5° south of east. Immediately after the inelastic collision,...
A cannonball of mass 25.1 kg is shot into the air at an angle of 45...
A cannonball of mass 25.1 kg is shot into the air at an angle of 45 degrees with respect to horizontal. At the top of its ballistic trajectory, the cannonball suddenly explodes into two separate pieces, a smaller piece this is 1/3 the original mass, and a larger piece that is 2/3 the original mass. The smaller piece ends up landing right back at the spot where the cannonball was originally launched, 29.8 seconds after it was launched. How far...
An object with total mass mtotal = 17.4 kg is sitting at rest when it explodes...
An object with total mass mtotal = 17.4 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 21° above the –x axis with a speed of v1 = 25.9 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 26° to the right of the -y axis...
A 4.0 kg projectile is launched into the air with an initial velocity of 15 m/s...
A 4.0 kg projectile is launched into the air with an initial velocity of 15 m/s at an angle of 30° above the horizontal. When the projectile reaches its maximum height it explodes, splitting in two parts, one of mass 3.0 kg and one of mass 1.0 kg. Assume the explosion was essentially instantaneous. Determine the maximum height of the projectile using energy. After the explosion, if the 1.0 kg mass is moving at 1/2 the speed it was right...
A tank, at rest at the origin of an x-y coordinate system, explodes into three pieces....
A tank, at rest at the origin of an x-y coordinate system, explodes into three pieces. Just after the explosion, one piece, mass of m, moves with the speed v in the negative x- direction, and a second piece, with mass m/2, moves with a speed vd at an angle of 30 degrees (down or -yaxis) with respect to the +x axis. The third piece with mass m/2 moves with speed vu at an angle (up or +y axis) of...
An object with total mass mtotal = 15.5 kg is sitting at rest when it explodes...
An object with total mass mtotal = 15.5 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.5 kg moves up and to the left at an angle of θ1 = 22° above the –x axis with a speed of v1 = 26.3 m/s. A second piece with mass m2 = 5.3 kg moves down and to the right an angle of θ2 = 27° to the right of the -y axis...
An object with total mass mtotal = 16.4 kg is sitting at rest when it explodes...
An object with total mass mtotal = 16.4 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.7 kg moves up and to the left at an angle of θ1 = 18° above the –x axis with a speed of v1 = 26.1 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of θ2 = 23° to the right of the -y axis...
A 37.0-kg body is moving in the direction of the positive x axis with a speed...
A 37.0-kg body is moving in the direction of the positive x axis with a speed of 243 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 10.0 kg, moves away from the point of explosion with a speed of 397 m/s along the positive y axis. A second fragment, whose mass is 3.5 kg, moves away from the point of explosion with a speed of 337 m/s along the negative x...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT