A 3.00kg projectile must be launched across a room so that it lands 8.50m from the launching point. If the ceiling height is 2.90m, can this be done? What force must be applied over a time of 0.111 sec and at what angle for the projectile to land 8.50m from the launching point?

You have two variables to play with: initial velocity of the projectile and angle of launch. Write out an equation for the time that the projectile spends in the air based on initial velocity and angle, and from that the horizontal distance it travels in that time. You should end up with an equation that relates the required angle to the initial velocity. Since the launch angle is not specified, you can pick a value and then determine the required initial velocity. Finally, determine the acceleration needed to reach that initial velocity in the time given, and use F=ma to get your final answer.