Question

A falling stone takes 0.28s to travel past a window 2.2m tall. From what height above the top of the window did the stone fall?

Answer 1

Answer: 1.815448 m

Step-by-step explanation:

Step 1:

Identify knowns & unknowns

This question is asking to find final height with knowns of initial height, initial velocity, and elapsed time.

Step 2: Identify the related formula. This is the formula used for problems related to Displacement after gravitational acceleration.

Xf = Xi + Vi t - 1/2gt^2

Xf - final height

Xi - initial height

Vi - initial velocity

t - elapsed time

g - gravitational acceleration constant

Step 3: Input variables, solve, and simplify.

The steps are in the image below.

Step 4: Check unit of measurement

Distance is measured in meters.

Answer 2

Using kinematic equations and the known time and height of the window, we can calculate the height from which the stone was dropped above the window. This involves determining the stone's velocity at the top of the window and using it to find the initial drop height.

Step-by-step explanation:

To determine the height from which the stone fell above the top of the window, we'll use the kinematic equations for uniformly accelerated motion, assuming acceleration due to gravity (g = 9.81 m/s2).

The stone takes 0.28 seconds to pass by a 2.2m tall window, which means the stone's average velocity (v_avg) while passing by the window can be calculated by dividing the window's height by the time taken:

V_avg = Height / Time = 2.2m / 0.28s ≈ 7.857 m/s

This average velocity is the midpoint of the stone's velocity as it enters and exits the window frame, since acceleration is constant. To find the velocity at the top of the window (v_top), we use the fact that v_avg = (v_top + v_bottom) / 2. Since v_bottom = v_top + g*t, we solve for v_top:

v_top = 2 * v_avg - v_bottom = 2 * v_avg - (v_top + g * t), which allows us to calculate the initial velocity at the top of the window.

Finally, we can determine the initial height from which the stone fell above the window using the kinematic equation v2 = u2 + 2*g*h, where v is the final velocity (velocity at the top of the window), u is the initial velocity (0 m/s when dropped), and h is the height.