A brick is thrown upward from the top of a building at an angle of 35° to the horizontal and with an initial speed of 14 m/s. If the brick is in flight for 3s, how tall is the building?

Vo = 14m/s[35o].

Yo = 14*sin35 = 8.03 m/s.

Y = Yo + g*Tr = 0 at max ht.
8.03 - 9.8Tr = 0,
Tr = 0.82 s. = Rise time.

Tf = Tr = 0.82 s. = Time to fall back to top of bldg.

T = 3-(0.82+0.82) = 1.36 s. = Time to fall from top of bldg. to gnd.

h = Vo*T + 0.5g*T^2.
Vo = 14 m/s, T = 1.36 s, g = + 9.8 m/s^2, h = ?.

To find the height of the building, we need to break down the motion of the brick into vertical and horizontal components.

First, let's find the vertical component of the brick's initial velocity. The initial speed of the brick, 14 m/s, can be decomposed into vertical and horizontal velocities using trigonometry. Since the angle of projection is 35°, the vertical velocity can be found using the sine function:

Vertical velocity (Vy) = initial speed (14 m/s) × sin(angle of projection)

Next, we know that the acceleration due to gravity acts vertically downward, causing a change in velocity in the vertical direction. We can use this acceleration and the time of flight to determine the change in the vertical velocity:

Change in vertical velocity (ΔVy) = acceleration due to gravity × time of flight

In this case, the time of flight is given as 3 seconds and we know that the acceleration due to gravity is approximately 9.8 m/s². So we have:

ΔVy = 9.8 m/s² × 3 s

Now, let's find the vertical displacement, which is the change in height of the brick:

Vertical displacement (Δy) = (initial vertical velocity + final vertical velocity) / 2 × time of flight

In this case, the final vertical velocity is equal to the initial vertical velocity minus the change in vertical velocity:

Final vertical velocity = initial vertical velocity - ΔVy

Now we can substitute the values we have and calculate the height of the building:

Δy = (initial vertical velocity + final vertical velocity) / 2 × time of flight

Remember that the initial vertical velocity is Vy and the final vertical velocity is Vy - ΔVy. So,

Δy = (Vy + (Vy - ΔVy)) / 2 × time of flight

Once you have calculated Δy, that will give you the height of the building.

I told you how to do this type of problem earlier.