Abrick lands 10.1 m from the base of a building. if it was given an initial velocity of 8.6 m/s [61º above the horizontal], how tall is the building?

First, we have to establish the reference system. Let's assume that the building is on the negative y-axis and that the brick was thrown at the origin (see figure attached).

According to this, the initial velocity has two components, because the brick was thrown at an angle :

  (1)

 (2)

  (3)

  (4)

As this is a projectile motion, we have two principal equations related:

 (5)

Where:

is the distance where the brick landed

is the time in seconds

If we already know and , we have to find the time (we will need it for the following equation):

 (6)

 (7)

  (8)

Where:

is the height of the building (in this case it has a negative sign because of the reference system we chose)

is the acceleration due gravity

Substituting the known values, including the time we found on equation (7) in equation (8), we will find the height of the building:

  (9)

  (10)

Multiplying by -1 each side of the equation:

>>>>This is the height of the building

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