Abaseball is hit with a speed of 27.0 m/s at an angle of 45.0o. it lands on the flat roof of a 13.0 m tall nearby building. if the ball was hit when it was 1.0 m above the ground, what horizontal distance does it travel before it lands on the building?

10.175 m

Explanation:

This situation is related to parabolic movement with constant acceleration (due gravity) and can be modeled by the following equations:

   (1)

   (2)

   (3)

Where:

 is the baseball's final height (when it lands on the building's roof)

is the  baseball's initial velocity

is the baseball's final velocity

is the time the parabolic movement lasts  until the baseball lands on the roof

 is the acceleration due to gravity

is the horizontal distance  the baseball travels

is the angle at which the baseball was hit

Let's begin finding  with (1):

   (4)

   (5)

   (6)

Substituting (6) in (2):

   (7)

Isolating :

   (8)

Substituting (8) in (3):

   (9)

Finally: