Question

a 1500 kg weather rocket accelerates upward at 10 m/s2 . it explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. photos reveal that the lighter frag- ment traveled straight up and reached a maximum height of 530 m. what were the speed and direction of the heavier fragment just after the explosion?

Answer 1

To find the speed and direction of the heavier fragment just after the explosion, we can use the principle of conservation of momentum. After the explosion, the lighter fragment travels straight up and reaches a maximum height of 530 m. Using the principle of conservation of momentum, we can equate the momentum of the lighter fragment to the momentum of the heavier fragment just after the explosion.

Step-by-step explanation:

To find the speed and direction of the heavier fragment just after the explosion, we can use the principle of conservation of momentum. Since the fragments separate after the explosion, their momenta must be equal and opposite. Let's assume the mass of the lighter fragment is m, so the mass of the heavier fragment is 2m. The initial momentum of the system is zero because the rocket was at rest before the explosion.

After the explosion, the lighter fragment travels straight up and reaches a maximum height of 530 m. We can use kinematic equations to find the initial velocity and time of flight for the lighter fragment. With that information, we can calculate its momentum.

Using the principle of conservation of momentum, we can equate the momentum of the lighter fragment to the momentum of the heavier fragment just after the explosion.