3. A cricket ball of mass 0.5 kg is struck by a bat. Immediately before being struck, the velocity of the ball is \(( - 30 \mathbf { i } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Immediately after being struck, the velocity of the ball is \(( 16 \mathbf { i } + 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Find the magnitude of the impulse exerted on the ball by the bat. In the subsequent motion, the position vector of the ball is \(\mathbf { r }\) metres at time \(t\) seconds. In a model of the situation, it is assumed that \(\mathbf { r } = \left[ 16 t \mathbf { i } + \left( 20 t - 5 t ^ { 2 } \right) \mathbf { j } \right]\). Using this model,
2. find the speed of the ball when \(t = 3\).