A brick is dropped from a high scaffold.
(a) What is its velocity after 4.5 s?
m/s
(b) How far does the brick fall during this time?
A brick falls freely from a high scaffold. What is its velocity after 4.0s?
bandbox
To answer these questions, we can use the equations of motion in one dimension.
The first equation is the equation of motion that relates the final velocity (Vf), initial velocity (Vi), acceleration (a), and time (t):
Vf = Vi + at
The second equation is the equation that relates the displacement (s), initial velocity (Vi), time (t), and acceleration (a):
s = Vi*t + (1/2)*a*t^2
Given:
Initial velocity (Vi) = 0 m/s (since the brick was dropped)
Acceleration (a) = 9.8 m/s^2 (acceleration due to gravity)
Time (t) = 4.5 s
(a) To find the velocity after 4.5 seconds, we can use the first equation:
Vf = Vi + at
Vf = 0 + (9.8)*(4.5)
Vf = 44.1 m/s
Therefore, the velocity of the brick after 4.5 seconds is 44.1 m/s.
(b) To find the distance the brick falls during this time, we can use the second equation:
s = Vi*t + (1/2)*a*t^2
s = 0*(4.5) + (1/2)*(9.8)*(4.5)^2
s = 0 + (1/2)*(9.8)*(20.25)
s = (1/2)*(9.8)*(20.25)
s = 99.45 m
Therefore, the brick falls a distance of 99.45 meters during this time.
To answer these questions, we can use the equations of motion for objects in free fall. Here's a step-by-step guide on how to calculate the velocity and distance for the falling brick.
Step 1: Identify the given information:
In this case, we are given that the brick has been falling for 4.5 seconds.
Step 2: Determine the acceleration due to gravity (g):
The acceleration due to gravity is approximately 9.8 m/s^2 on Earth. We assume that the air resistance is negligible, so the acceleration remains constant throughout the fall.
Step 3: Calculate the velocity after 4.5 seconds (a):
To find the velocity, we use the formula:
v = u + at
where u is the initial velocity (which is zero since it was dropped), a is the acceleration due to gravity, and t is the time.
In this case, the initial velocity (u) is zero because the brick is dropped from rest. The time (t) is 4.5 seconds, and the acceleration (a) is -9.8 m/s^2 (negative because it acts in the opposite direction to the motion).
Substituting the values into the formula:
v = 0 + (-9.8) * 4.5
Solving the equation:
v = -44.1 m/s
Therefore, the velocity of the brick after 4.5 seconds is -44.1 m/s. The negative sign indicates that the velocity is directed downwards.
Step 4: Calculate the distance the brick falls (s):
To calculate the distance fallen, we use the formula:
s = ut + (1/2) * a * t^2
where u is the initial velocity (0 m/s), t is the time (4.5 seconds), and a is the acceleration due to gravity (-9.8 m/s^2).
Substituting the values into the formula:
s = 0 * 4.5 + (1/2) * (-9.8) * (4.5)^2
Solving the equation:
s = -99.225 meters (approximately)
Therefore, the brick falls approximately 99.225 meters during 4.5 seconds.
(a) The velocity after 4.5 seconds is -44.1 m/s.
(b) The distance the brick falls during this time is approximately 99.225 meters.