# Acceleration Due to Gravity, Time and Horizontal Velocity

1. (PART ONE OF TWO): You drop a stone from a position of rest. How far will it fall vertically in the ?rst 5 s?

The acceleration of gravity is 9.8 m/s.

2. ( PART TWO OF TWO): If you instead toss it horizontally at 1.6 m/s, how far will it fall vertically in the ?rst 5 s?

3. A cat chases a mouse across a 1.7 m high table. The mouse steps out of the way, and the cat slides o? the table and strikes the ?oor 2.8 m from the edge of the table. The acceleration of gravity is 9.81 m/s.

What was the cat's speed when it slid o? the table?

4. Cli? divers at Acapulco jump into the sea from a cli? 37.1 m high. At the level of the sea, a rock sticks out a horizontal distance of 14.25 m. The acceleration of gravity is 9.8 m/s. With what minimum horizontal velocity

must the cli? divers leave the top of the cli? if they are to miss the rock?

5. (PART ONE OF TWO ) A toy car runs o? the edge of a table that is 1.78 m high. The car lands 0.4255 m from the base of the table. How long does it take for the car to fall? The acceleration due to gravity is 9.8 m/s.

6. (Part TWO OF TWO) What is the horizontal velocity of the car?

#### Solution Preview

All of these questions have to do with acceleration due to gravity, time and horizontal velocity. First, let's consider some basic logic. We know that an object that falls from rest, like in question 1, will accelerate towards the ground at the rate defined by the acceleration due to gravity. It takes time to accelerate the object and for it to reach the ground. During this time, if the object started off perfectly still, it would simply travel that vertical distance.

Let's consider the first question.

We can figure out this time using kinematic equations. Firstly, let's consider what we know:

v0 ...

#### Solution Summary

The following posting helps with problems involving acceleration due to gravity, time and horizontal velocity.