A 0.72 kg rock is projected from the edge of the top of a building with an initial velocity of 11 m/s at an angle 51◦ above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 17.4 m from the base of the building. how tall is the building? gravity is 9.8 m/s/s

To find the height of the building, we need to calculate the time it takes for the rock to hit the ground. We can then use this time to calculate the vertical distance traveled by the rock.

Step 1: Calculate the time of flight:
The horizontal motion of the rock is independent of the vertical motion. Therefore, we can calculate the time of flight using the horizontal distance traveled by the rock.

The horizontal distance traveled (17.4 m) is equal to the horizontal component of the initial velocity (11 m/s) multiplied by the time of flight:
17.4 m = 11 m/s * time of flight

Rearranging the equation gives:
time of flight = 17.4 m / 11 m/s

Step 2: Calculate the vertical distance traveled:
To find the height of the building, we need to calculate the vertical distance traveled by the rock during the time of flight.

The vertical distance traveled can be found using the formula:
vertical distance = vertical component of initial velocity * time + (1/2) * acceleration due to gravity * time^2

The vertical component of the initial velocity can be found using the equation:
vertical component = initial velocity * sin(angle)

Substituting the known values into the formula:
vertical distance = (11 m/s * sin(51°)) * (17.4 m / 11 m/s) + (1/2) * (9.8 m/s^2) * (17.4 m / 11 m/s)^2

Step 3: Calculate the height of the building:
The height of the building is equal to the vertical distance traveled by the rock.

Substitute the calculated values into the equation:
height = (11 m/s * sin(51°)) * (17.4 m / 11 m/s) + (1/2) * (9.8 m/s^2) * (17.4 m / 11 m/s)^2

Calculating this equation will give you the height of the building.