Magnitude of Acceleration

1. What is the magnitude of the acceleration of a 65-kg skier moving down a hill that makes a 51 ? angle with the horizontal? Ignore friction. Express answer with appropriate units.2. A cannon ball is shot straight up at an initial speed of 98 m/s. The unit vector (j^) is directed upwards.          a). What is the speed of the cannon ball at 7.0s?          b). What is the velocity of the cannon ball at 7.0s?          c). What is the speed of the cannon ball at 10s?          d).What is the velocity of the cannon ball at 10s?          e). What is the speed of the cannon ball at 13s?          f).What is the velocity of the cannon ball at 13s?          g). What is the speed of the cannon ball at 20s?          h).What is the velocity of the cannon ball at 20s?3. A 2.0-kg cart collides with a 1.0-kg cart that is initially at rest on a low-friction track. After the collision, the 1.0-kg cart moves to the right at 0.35 m/s and the 2.0-kg cart moves to the right at 0.30 m/s .          If the positive direction is to the right, what was the initial velocity of the 2.0-kg cart?4. A 1-kg standard cart collides with a 4.5-kg cart initially at rest on a low-friction track. After the collision, the standard cart is at rest and the 4.5-kg cart has a velocity of 1.4 m/s to the left.         What was the initial velocity of the standard cart? Suppose that the positive direction is the direction to the right.5. You drop a 0.20-kg ball to the floor from a height of 2.9 m , and it bounces to a height of 1.9 m .          What is the magnitude of the change in its momentum as a result of the bounce?6. A load of coal is dropped from a bunker into a railroad hopper car of inertia 2.0 × 104kg coasting at 0.70 m/s on a level track. The car’s speed is 0.50 m/s after the coal falls.          What is the inertia (mass) of the load of coal?7. A 400-kg shipboard cannon fires a 50-kg ball at 60 m/s. The cannon’s resulting recoil speed across the deck is regarded as excessive.          How much mass (in the form of sandbags, say) must be added to the cannon if its recoil speed must be reduced to 2.0 m/s?8. Two carts collide on a low-friction track. Cart 1 has an initial momentum of +10 kg?m/s?^ and a final momentum of -3.0 kg?m/s?^ .        If cart 2 has a final momentum of -5.0 kg?m/s?^ , what was its initial momentum?

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