Question

In: Physics

A 1246 kg weather rocket accelerates upward at 11.7 m/s2. It explodes 1.6 s after liftoff...

A 1246 kg weather rocket accelerates upward at 11.7 m/s2. It explodes 1.6 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 571 m. What were the speed of the heavier fragment just after the explosion?

Solutions

Expert Solution

M = 1246
Let the two fragments be , m1 & m2
Given , m1 = 2 * m2
m1 + m2 = 1246 kg
2 m2 + m2 = 1246
m2 = 1246/3 = 415.33 kg
m1 = 830.7 kg

The speed of the rocket 1.6 s after take off is :

( 11.7 m/s^2)* ( 1.6 s) = 18.72 m/s

before collision : 18.72 m/s at 1246 kg

after collision : V1 at 500 kg and V2 at 1000 kg

we can determine V1 using kinematics:

the height of the rocket at explosion is:

yi = 1/2 a ( t^2)

    = (1/2) * (11.7)* (1.6)^2

     = 15 m

the final height of the light fragment is 571m, so

(Vf)^2 - (V1)^2 = 2ay

0 - (V1)^2 = 2*(- 9.8) *(571 - 18.72)

      Vf = square root (2*9.8*552.28)

            104.04m/s

By conservation of momentum at the exploision :

      1246* (18.72) = 830.7*(104.04) +415.3 V2

1246 * 18.72 = m1 * v1 + m2 * v2
1246 * 18.72 = 830.7 * v1 + 415.3 * 104.04
v1 = - 23.93 m/s ( i.e downward)

I hope help you.....!!


Related Solutions

2. A rocket is fired vertically with an upward acceleration of 20 m/s2. After 25 s,...
2. A rocket is fired vertically with an upward acceleration of 20 m/s2. After 25 s, the engine shuts off and the rocket continues as a free particle. (a) Find the highest point the rocket reaches. (b) Find the total time the rocket is in the air. (c) Draw the graph acceleration versus time for the motion. d) Draw the graph velocity versus time for the motion. (e) Draw the graph position versus time for the motion. (f) On each...
An elevator accelerates upward at 1 m/s2. When the elevator is moving upward at 2 m/s,...
An elevator accelerates upward at 1 m/s2. When the elevator is moving upward at 2 m/s, a bolt drops from the ceiling which is 2.5 m above the ?oor. Assume that the bolt does not experience air resistance. Calculate how long it takes for the bolt to hit the ?oor, how far it travels, and how fast it is going when it hits the ?oor of the elevator. Solve this problem in two reference frames, one ?xed with respect to...
A 500 kg elevator accelerates upward at 1.9 m/s2 for 20 m, starting from rest. a)...
A 500 kg elevator accelerates upward at 1.9 m/s2 for 20 m, starting from rest. a) How much work does gravity do on the elevator? b) How much work does the tension in the elevator cable do on the elevator? c) What is the elevator’s kinetic energy after traveling 20 m?
A model rocket is launched straight upward with an initial speed of 42.0 m/s. It accelerates...
A model rocket is launched straight upward with an initial speed of 42.0 m/s. It accelerates with a constant upward acceleration of 2.50 m/s2 until its engines stop at an altitude of 160 m. (a) What can you say about the motion of the rocket after its engines stop?. (b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?
a model rocket is launched straight upward with an innitial speed of 11.0 m/s. it accelerates...
a model rocket is launched straight upward with an innitial speed of 11.0 m/s. it accelerates with a constant upward acceleration of 22 m/s^2 until its engines stop 3.0 seconds later. it then continues on as a free fall particle until it hits the ground. (a) draw and label a diagram of the above and below information (b) find the velocity (in m/s ) of the rocket at the instant it runs out if fuel. (c)find the max height (in...
The acceleration of a rocket traveling upward is given by a = (8 + 0.02s) m/s2,...
The acceleration of a rocket traveling upward is given by a = (8 + 0.02s) m/s2, where s is in meters.(Figure 1). Initially, v = 0 and s = 0 when t = 0. Determine the time needed for the rocket to reach an altitude of s = 100 m .
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 is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It...
A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back to Earth. (a) Find the rocket’s height when it runs out of fuel; (b) find the rocket’s velocity when it runs out of fuel; (c) find the maximum height the rocket reaches; (d) find the rocket’s velocity the instant before the rocket...
A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0...
A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0 m/s2 until it reaches a speed of 1.50×102 m/s when the engines are cut off. After that the rocket is in free-fall. What is the maximum height reached by the rocket ? What total time elapses between take-off and the rocket hitting the ground?
A 2290 kg car traveling at 11.7 m/s collides with a 2620 kg car that is...
A 2290 kg car traveling at 11.7 m/s collides with a 2620 kg car that is initially at rest at the stoplight. The cars stick together and move 3.30 m before friction causes them to stop. Determine the coefficient of kinetic friction betwen the cars and the road, assuming that the negative acceleration is constant and that all wheels on both cars lock at the time of impact.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT