A baseball player bats a ball at a speed of 90.0 ft/sec at an angle of 40.0 degrees in an indoor baseball stadium. The roof is 90.0 feet high.

What is the total time that the baseball is in the air?

Question

A baseball player bats a ball at a speed of 90.0 ft/sec at an angle of 40.0 degrees in an indoor baseball stadium. The roof is 90.0 feet high. 

What is the total time that the baseball is in the air?

anonymous · Answer

Because of the symmetry of the problem, the total time of flight will be twice the time it takes for the ball to reach it's highest point.  To find this, we need the vertical component of the speed.  We get this as shown in the drawing:|dw:1353078314614:dw|So $$v_y=90\sin 40=57.85$$Now we have a one dimensional problem of a ball going up with a speed of 57.85m/s under a constant force of gravity F=-mg
Can you take it from here?$$v_f=v_i+at$$Here vf=0, vi=57.85 and a=-9.81.  Solve for t.  Don't forget to multiply this by two to get the total time of flight.