Question

In: Physics

A model rocket is shot straight up and explodes at the top of its trajectory into...

A model rocket is shot straight up and explodes at the top of its trajectory into three pieces as viewed from above and shown in the figure below. The masses of the three pieces are

m_A = 125.0 g,

m_B = 20.0 g,

and

m_C = 30.0 g.

Immediately after the explosion, piece A is traveling at 1.40 m/s, and piece B is traveling at 6.90 m/s in a direction 30° below the negative x axis as shown. What is the velocity of piece C?

magnitude	____m/s
direction	_____° below the positive x axis

Expert Solution

fiven

ma = 0.125 kg

mb = 0.02 kg

mc = 0.03 kg

take xaxis as i

y axis as j

z axis as k

from conservation of monentum

total initial momentum = total final momentum

o = mava+mbvb+mcvc

0 = 0.125*1.4(j)+0.02*(6.9cos30(-i)+6.9sin30(-j)+0.03*vc

0 = 0.175 j-0.119i-0.069j+0.03vc

0.03vc = 0.119i-0.106j

vc = 3.97 i-3.53 j

this is the velocity of piece c

magnitude = vc = sqrt(3.97^2+(-3.53)^2) = 5.31 m/s

direction = theta = tan^-1(-3.53/3.97) = 41.64 degrees below the positive x axis

genius_generous answered 2 years ago

During a fireworks display, a 0.300-kg bottle rocket approaches the top of its trajectory and explodes...

During a fireworks display, a 0.300-kg bottle rocket approaches the top of its trajectory and explodes into two pieces as in the figure. The first piece (Piece 1) has mass 0.200 kg and the second piece (Piece 2) has mass 0.100 kg. Immediately after the explosion, the first piece is observed traveling to the left at a speed of 4.20 m/s and the second piece is observed traveling at an angle θ = 32.0° above the horizon at a speed...

A rocket of M = 20 kg moves in a straight line upwards and explodes 50...

A rocket of M = 20 kg moves in a straight line upwards and explodes 50 meters above the ground, separating into two fragments that are launched horizontally. One of the fragments, with a mass equal to two-thirds of the mass of the rocket, falls ten meters from the launch point. a) How far does the other fragment fall? b) At what speed does the lightest fragment reach the ground? c) If the explosion produces 300 J as heat, what...

A rocket shot up reaches a height of 90.0m where an explosion causes the rocket to...

A rocket shot up reaches a height of 90.0m where an explosion causes the rocket to split into two parts that weigh 2.8kg and 0.56kg respectively. 870J of chemical energy was transformed into kinetic energy of the two parts. (i) Describe the conservation of momentum and energy and include an equation that represents this example. (ii) What is the speed of each part just after the explosion? (iii) It is observed that the two parts hit the ground at the...

A 1000 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration...

A 1000 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 3600 m. You can ignore any effects of air resistance. What was the rocket's acceleration during the first 16 s?

A fireworks rocket is launched vertically upward at 40 m/s. At the peak of its trajectory,...

A fireworks rocket is launched vertically upward at 40 m/s. At the peak of its trajectory, it explodes into two equal-mass fragments. One reaches the ground t1 = 2.63s after the explosion. When does the second fragment reach the ground?

A ball of mass m is shot straight up into the air by a spring-loaded launcher....

A ball of mass m is shot straight up into the air by a spring-loaded launcher. Initially, the spring is compressed by a distance D. After the spring is released, the ball has a velocity v out of the launcher and finally reaches a maximum height H. Ignoring air resistance, which of the following statements are true? True False If the spring constant is doubled, the ball will max out at height 8H True False The initial potential energy of the spring...

A projectile is shot straight up from the earth's surface at a speed of 5000km/hr ....

A projectile is shot straight up from the earth's surface at a speed of 5000km/hr . How high does it go? Express your answer with the appropriate units.

An arrow is shot straight up in the air with an initial speed of 240 ft/s....

An arrow is shot straight up in the air with an initial speed of 240 ft/s. If on striking the ground it embeds itself 8.00 in into the ground, find the magnitude of the acceleration (assumed constant) required to stop the arrow, in units of feet/second^2.

An arrow is shot straight up from a horizontal level with an initial velocity of 45j...

An arrow is shot straight up from a horizontal level with an initial velocity of 45j m/s. A. Find its flight time. B. Find its position at t=6.0s C. What is its velocity at t=6.0s D. Graph v(t) vs. t.

A model rocket is fired from the ground in a parabolic arc. At the very top...

A model rocket is fired from the ground in a parabolic arc. At the very top of the arc, at a horizontal displacement of 260 m from the launch point, an explosion occurs within the rocket, breaking it into two fragments which separate from each other. One fragment, having 1/3 the mass of the rocket, falls straight down to Earth as if it were at rest at that moment right after the explosion. Determine the total horizontal displacement from the launch...