Kenny Klutz drops his physics book off his aunt's high rise balcony. It hits the ground below 1.5s later.

a. With what speed does it hit?
b. How high is the balcony?
(Ignore the air drag)

V = g t = 14.7 m/s

H = (g/2) t^2

t = 1.5 s
Solve for H (the height)

To determine the answers to these questions, we can use the equations of motion under constant acceleration. In this case, the acceleration will be due to gravity.

Let's break down the problem step by step:

Step 1: Determine the time it takes for the physics book to hit the ground.
Given: The time it takes for the book to hit the ground is 1.5 seconds.

Step 2: Determine the acceleration due to gravity.
We know that the acceleration due to gravity near the Earth's surface is approximately 9.8 m/s^2.

Step 3: Use the time and the acceleration of gravity to find the final velocity of the book.
We can use the equation for motion with constant acceleration: v = u + at. Since the book starts from rest (u = 0), the equation simplifies to v = at. Plugging in the given values, we have v = (9.8 m/s^2) × (1.5 s).

a. With what speed does the book hit the ground?
To find the speed at which the book hits the ground, we substitute the values into the equation v = (9.8 m/s^2) × (1.5 s) and calculate the result.

Step 4: Calculate the height of the balcony.
We can use another equation of motion: h = ut + (1/2)gt^2, where h is the height, u is the initial velocity (which is 0 since the book is dropped), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken (1.5 s).
Since the initial velocity is 0, the equation simplifies to h = (1/2)gt^2.

b. How high is the balcony?
To find the height of the balcony, we substitute the values into the equation h = (1/2) × (9.8 m/s^2) × (1.5 s)^2 and calculate the result.

By following these steps, you should be able to find the answers to both parts of the question.

To address this problem, let's assume the following:

- Acceleration due to gravity is approximately 9.8 m/s².
- The initial velocity (in this case, from the release) is zero.

a. With what speed does the book hit the ground?
To solve for the final velocity (v), we can use the kinematic equation:
v = u + a*t

Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 9.8 m/s²
Time (t) = 1.5 s

Substituting these values into the equation:
v = 0 + (9.8 * 1.5)
v ≈ 14.7 m/s

Therefore, the book hits the ground with a speed of approximately 14.7 m/s.

b. How high is the balcony?
To determine the height of the balcony (h), we can use another kinematic equation:
h = u*t + (1/2)*a*t²

Substituting the given values:
h = 0*1.5 + (1/2)*9.8*(1.5)²
h = 0 + (1/2)*9.8*(2.25)
h ≈ 10.1 m

Therefore, the height of the balcony is approximately 10.1 meters.