How to keep a portion of your brain alert while sleeping

Two polarizers are oriented at 70∘∘ to one another. unpolarized light falls on them. what fraction of the light intensity is transmitted?

During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. if the trebuchet launches the stones with a velocity of at an angle of 50.0°, (a) how long does it take the stone to hit the ground? (b) what is the maximum distance that the trebuchet can be from the castle wall to be in range? (c) how high will the stones go? show all your work.

The pilot of a helicopter hovers at an altitude of 1200 feet over a park. the angle of depression to the base of a statue is 17 degrees. the angle of depression to the nearest park exit, in line with the statue, is 14 degrees. to the nearest foot, what is the distance from the statue to the exit?