Free Fall Building Height Calculation
Problem Analysis
The problem involves a ball in free fall, starting from rest. We are given the final velocity reached and the acceleration due to gravity. We need to determine the height from which the ball fell, which corresponds to the height of the building.
- Initial velocity (\(u\)): \(0\text{ m/s}\) (since the ball starts from rest)
- Final velocity (\(v\)): \(40\text{ m/s}\) (maximum velocity reached)
- Acceleration (\(a\)): \(g = 10\text{ m/s}^2\) (acceleration due to gravity)
- Displacement (\(s\)): Height of the building (\(h\)), which needs to be calculated.
Kinematic Equation for Height
We can use a standard kinematic equation that relates initial velocity, final velocity, acceleration, and displacement. The appropriate equation is:
\(v^2 = u^2 + 2as\)
Calculation Steps
Substitute the known values into the kinematic equation:
\((40\text{ m/s})^2 = (0\text{ m/s})^2 + 2 \times (10\text{ m/s}^2) \times h\)
Simplify the equation:
\(1600\text{ m}^2/\text{s}^2 = 0 + (20\text{ m/s}^2) \times h\)
\(1600\text{ m}^2/\text{s}^2 = (20\text{ m/s}^2) \times h\)
Now, solve for the height (\(h\)):
\(h = \frac{1600\text{ m}^2/\text{s}^2}{20\text{ m/s}^2}\)
\(h = 80\text{ m}\)
Therefore, the height of the building is 80 meters.
Similar Questions
- A ball thrown up vertically returns to the ground after 10 second. Find the velocity with which it was thrown up? (if g = 10 m/s2).
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Important Questions from Kinematic equations for uniformly accelerated motion
Which of the following is an equation of motion?
I. u = v + at
II. 2as = v 2– u 2
- A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately
- A ball thrown up vertically returns to the ground after 10 second. Find the velocity with which it was thrown up? (if g = 10 m/s2).
If the distance travelled by a body in the $n^{th}$ second is given by $(7 + 5n)$ m, then find the initial velocity and acceleration of the body respectively.
Which of the following is an equation of motion?
I. u = v + at
II. 2as = v 2– u 2
