Push-Away Problems Practice Problems

A satellite with a mass of 5.0 × 10⁶ kg is moving at a speed of 2.5 × 10⁶ m/s. Due to a major technical issue, the satellite explodes into 3 fragments. One of the fragments with a mass of 7.5 × 10⁵ kg continues forward at a speed of 1.5 × 10⁶ m/s. The second fragment moves in the backward direction at a speed of 0.5 × 10⁶ m/s. Find the speed and direction in which the third fragment moves, if the mass of the second fragment is 6.0 × 10⁵ kg.

During a laboratory session, a student pushes a 500 g small vehicle against an ideal massless spring welded to a 1500 g truck. Initially, the car and the truck are not moving. The student releases the vehicle and measures, using a motion detector, that the vehicle moves at a speed of 0.5 m/s relative to a frame attached to the truck. Find the speed of the vehicle relative to earth.

A rocket experienced a launch anomaly and exploded into four parts. The first part has a mass of 4000 kg and a velocity of 7.5 km/s ĵ. The second part has a mass of 3500 kg and a velocity of 1.1 km/s î +4.5 km/s ĵ. The third part has a mass of 5000 kg and a velocity of -1.2  km/s î +3.5 km/s ĵ. The velocity of the fourth part of mass 500 kg is -0.5 km/s ĵ. Calculate the velocity of the rocket prior to the explosion.

A stationary body undergoes an explosion breaking into 3 fragments. Determine the momentum of the third fragment if the momentum of the two parts is as depicted in the figure below.

A man having a mass of 55 kg is riding a bike weighing 30 kg. There is a box with a mass of 15 kg kept on the rear seat of the bike. The man is initially riding the bike at 9.0 m/s and suddenly increases the speed to 12.0 m/s. Due to this, the box falls behind the bike. Determine the velocity of the falling box immediately after it falls off of the bike.

During a military test, a 1200 kg missile is launched with an acceleration of 12 m/s² in a vertically positive direction. However, the test fails and the missile blasts 3.0 s after its launch into two pieces before reaching the destination. One of the broken pieces was thrice as large as the other. The heavier piece moved vertically up to a height of 1430 m. Determine the velocity of the lighter piece.

A truck having a mass of 500 kg is travelling towards the east with a speed of 8.0 m/s. A fiber optic cable roll weighing 120 kg is placed on the truck. The cable roll suddenly rolls towards the back end of the truck with a speed of 1.5 m/s relative to the truck. Calculate the new speed of the truck.

Determine the distance between two space explorers, one weighing 55 kg and the other 75 kg including their spacesuits, after they push away from each other and the lighter explorer has traveled 11 m from their initial stationary position in space.

A cannon shot a cannonball. The force applied on the cannonball over the length of the barrel can be modeled by F = [890 - (5.7 x 10⁵ s^-1) t] N. The model is only valid for t ranging from t = 0 to t = 2.0 x 10^-3 s. As a result of the impulse given to the cannonball, it came out of the barrel of the cannon with a speed of 120 m/s. If the mass of the cannonball was 3.0 kg and the mass of the cannon was 500 kg, calculate the speed with which the cannon recoiled after firing.

A 115 kg person is stationary at the back of a 9.10 x 10³ kg bus moving forward horizontally at a speed of 5.00 m/s. Suddenly he starts moving toward the front of the bus, with a speed of 1.00 m/s relative to the bus. Given that the bus is 1.40 x 10¹ m long, determine how much the bus moves in the time it takes for the person to reach the front of the bus.

Determine the mass of gas that needs to be ejected if a 211 kg spacewalker (including the suit and oxygen tank) wants to return to his spacecraft at a velocity of 3.0 m/s, given that his oxygen tank can expel gas at 36 m/s.

A firefighter is standing on a 40.0-kg flatbed cart that is initially at rest on a frictionless surface. The firefighter has a mass of 60.0 kg. He throws a 7.0-kg fire extinguisher horizontally with a speed of 8.0 m/s to a fellow firefighter standing nearby. Calculate the velocity of the cart immediately after the extinguisher is thrown, assuming it was initially at rest.

A rocket with a total mass (including fuel) of 5000 kg is floating in space at a velocity of 200 m/s relative to an asteroid when it suddenly ejects a portion of its fuel with a mass of 500 kg to increase its velocity relative to that asteroid up to 250 m/s. Ignoring any external forces acting on this system over this small interval time needed for this action (the impulse approximation), what would be the fuel’s ejection speed relative to the rocket?