1 An eagle has caught a salmon of mass 3 kg to take to its nest. When the eagle is flying with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it drops the salmon. The salmon falls a vertical distance of 13 metres back into the sea. The salmon is to be modelled as a particle. The salmon's weight is the only force that acts on it as it falls to the sea.

1. Calculate the kinetic energy of the salmon when it is dropped by the eagle.
2. Calculate the potential energy lost by the salmon as it falls to the sea.
3. 1. Find the kinetic energy of the salmon when it reaches the sea.
   2. Hence find the speed of the salmon when it reaches the sea.
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      \(2 \quad\) A particle has mass 6 kg . A single force \(\left( 24 \mathrm { e } ^ { - 2 t } \mathbf { i } - 12 t ^ { 3 } \mathbf { j } \right)\) newtons acts on the particle at time \(t\) seconds. No other forces act on the particle.
4. Find the acceleration of the particle at time \(t\).
5. At time \(t = 0\), the velocity of the particle is \(( - 7 \mathbf { i } - 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). Find the velocity of the particle at time \(t\).
6. Find the speed of the particle when \(t = 0.5\).