Atoy robot is lauched at an intiial velocity of 80 ft/sec at an angle of 80 degrees with the horizontal. how long will it take the rocket to be 10 feet horizontally from its starting point? what will its vertical distance be at that point?

The robot has acceleration vector

where is the acceleration due to gravity.

Its initial velocity is

so that its velocity at time is

If we take the robot's starting position to be the origin, so that , then its position vector at time is

The rocket is 10 feet horizontally away from its starting point when

At this point, its vertical position is

above the ground.