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 15 m/s. If the brick is in flight for 2.7 s, how tall is the building?
hf=hi+vi'*t-4.9t^2
solve for hi, hf=o, vi=15sin35, t=2.7
To find the height of the building, we can break down the motion of the brick into horizontal and vertical components.
Step 1: Find the vertical component of the initial velocity.
The vertical component of the initial velocity is given by:
Viy = Vi * sin(θ)
Where Viy is the vertical component of the initial velocity, Vi is the initial velocity (15 m/s), and θ is the angle of projection (35°).
So, Viy = 15 * sin(35°)
Viy ≈ 8.53 m/s
Step 2: Find the time of flight.
The time of flight is given as 2.7 seconds.
Step 3: Find the vertical distance traveled.
The vertical distance traveled is given by the equation:
Y = Viy * t + (1/2) * g * t^2
Where Y is the vertical distance traveled, Viy is the vertical component of the initial velocity (8.53 m/s), t is the time of flight (2.7 seconds), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Y = 8.53 * 2.7 + (1/2) * 9.8 * (2.7)^2
Y ≈ 65.65 m
Therefore, the height of the building is approximately 65.65 meters.
To find the height of the building, we need to determine the vertical displacement of the brick during its flight. The vertical motion of the brick can be broken down into two components: an initial vertical velocity and a vertical acceleration due to gravity.
First, let's find the initial vertical velocity (v0y) of the brick. In this case, the initial velocity can be determined using the initial speed and the angle of projection.
v0y = v0 * sin(θ)
where v0 is the initial speed and θ is the angle of projection.
v0y = 15 m/s * sin(35°)
v0y = 15 m/s * 0.574 = 8.61 m/s (rounded to two decimal places)
Now, let's find the vertical displacement (Δy) of the brick using the equation:
Δy = v0y * t + (1/2) * g * t^2
where t is the time of flight and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Δy = 8.61 m/s * 2.7 s + (1/2) * 9.8 m/s^2 * (2.7 s)^2
Δy = 23.3 m + 35.59 m
Δy = 58.89 m (rounded to two decimal places)
Therefore, the height of the building is approximately 58.89 meters.