SOLUTION: a baseball player player hits a pitched a ball when it is 4 ft above the ground. The initial upward velocity is 80 ft/s. How long will it take for the ball to hit the ground

Algebra ->  Length-and-distance -> SOLUTION: a baseball player player hits a pitched a ball when it is 4 ft above the ground. The initial upward velocity is 80 ft/s. How long will it take for the ball to hit the ground      Log On


   

Question 1022423: a baseball player player hits a pitched a ball when it is 4 ft above the ground. The initial upward velocity is 80 ft/s. How long will it take for the ball to hit the ground
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-16t%5E2+%2B+80t+%2B+4+
+h%28t%29+ is the height at whatever time +t+ is
+-16t%5E2+ is due to downward pull of gravity
+80t+ is upward velocity
+4+ is initial height
------------------------
You want to find when +h%28t%29+=+0+, because that
is the ground level
+0+=+-16t%5E2+%2B+80t+%2B+4+
+0+=+-4t%5E2+%2B+20t+%2B+1+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+20+
+c+=+1+
+t+=+%28+-20+%2B-+sqrt%28+20%5E2+-+4%2A%28-4%29%2A1+%29%29+%2F+%282%2A%28-4%29%29+
+t+=+%28+-20+%2B-+sqrt%28+400+%2B+16+%29%29+%2F+%28-8%29+
+t+=+%28+-20+%2B-+sqrt%28+416+%29%29+%2F+%28-8%29+
+t+=+%28+-20+-+20.396+%29+%2F+%28-8%29+
( note that I used the negative square root so
that I would end up with positive time )
+t+=+%28+-40.396+%29+%2F+%28-8%29+
+t+=+5.05 sec
The ball hits ground in 5.05 sec
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+120%2C+-16x%5E2+%2B+80x+%2B+4+%29+
Hope I got it!