The Mars Pathfinder spacecraft used large airbags to cushion its impact with the planet’s surface when landing. Assuming the spacecraft had an impact velocity of 18.5 m/s at an angle of 45° with respect to the horizontal, the coefficient of restitution is 0.85 and neglecting friction, determine (a) the height of the first bounce, (b) the length of the first bounce. (Acceleration of gravity on Mars = 3.73 m/s2.)

Ball B is hanging from a cord of negligible weight. An identical ball A is measured 3m above the hanging ball and just touching the cord, is released from rest and acquires a velocity (V_o) before striking ball B. Assuming perfectly elastic impact and no friction, compute the  A) magnitude of the velocity of ball A in terms of V_o or velocity before impact B.) direction of the velocity of ball A in terms of V_o or velocity before impact (note: should be in angle with respect to north, east, west, south)

A rifle has mass M = 3 kg and fires a bullet of mass m = 10 g with muzzle velocity u = 700 m s-'. What is the recoil velocity v of the gun? From what height h would you have to drop the rifle on to your shoulder to feel the same kick?

(1) A car with mass 996 kg moving at 28 m/s hits a giant bag of marshmallows.  The bag slows the car down, but it is unable to completely stop it because it ruptures at Dt = 1.8 s after the car hits, scattering marshmallows all over the countryside.  Suppose the bag exerts a force on the car that depends on time (t) given by F = -At2; A = 7.2 x 103 N/s2 when t is in seconds   (2) Two objects, moving towards each other with speed v, collide head on, stick together, and then move on with speed v/4 after the collision. (a) What is the ratio of the kinetic energy after the collision to the kinetic energy before the collision? (answer: 1/16) (b) What is the ratio of the mass of the more massive object to the mass of the less massive object? (answer: 5/3)

A bullet enters the block with a velocity V0 = 250 m / s at X = 0 and travels 10 cm before stopping totally. If the velocity of the projectile is defined as V =V0 - kX, where V and X are in m / s and m respectively, determine a) the deceleration of the bullet, b) the time required for the bullet to travel 8 cminside the block

A ball of mass 0-80kg, moving with a speed of 5-0ms-1, collides with a wall at an angle of 40° to the normal to the wall. It rebounds with no change of speed and at the same angle to the normal. The duration of the impact is 0-15s. Find each of the following. (a) The average acceleration of the ball during the impact. (b) The average force on the ball during impact. (c) The average force on the wall during the impact.

Problem 8: A bullet is fired horizontally into an initially stationary block of wood suspended by a string and remains embedded in the block. The bullet's mass is m = 0.0095 kg, while that of the block is M = 1.03 kg. After the collision the block/bullet system swings and reaches a maximum height of h = 0.85 m above its initial height. Neglect air resistance.

A 0.350 kg hammer is moving horizontally at 5.50 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. Assume constant acceleration of the hammer-nail pair. (a) Calculate the duration of the impact (in s). (b) What was the average force (in N) exerted on the nail? (Enter the magnitude.)

First, find the magnitude of v that is, the speed v of the two-car unit after the collision.