A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the rider, wagon, and rock is 91 kilogram. The mass of the rock is 0.25 kilogram. Initially the wagon is rolling forward at a speed of 0.53 m/s. Then the person throws the rock with a speed of 16m/s. Both speeds are relative to the ground. Determine the speed of the wagon after the rock is thrown
(a) directly forward in one case and
(b) directly backward in another.