## Introduction

• Free-fall motion refers to the motion of an object under the influence of the Earth’s gravitational field without air resistance and other frictional forces.

• Such an object will experience an acceleration due to the gravitational force of the Earth, manifested as its weight. The magnitude of this acceleration is denoted by $g$, typically called the acceleration of free-fall.

• Although $g$ varies from $9.78~$m/s$^2$ to $9.83~$m/s$^2$ near the surface of the Earth depending on latitude, altitude, underlying geological formations, and local topography, the average value of $9.80~$m/s$^2$ will be used in this course, unless specified otherwise.

• Since the weight of an object is always pointing downward (towards the Earth’s center), the direction of the acceleration of free-fall is always vertically downward.

## Examples

EXAMPLE 1: A ball thrown straight up.

A ball thrown straight up with an initial velocity of $15.0~$m/s. Calculate the displacement and velocity at times of:

(a) $0.50~$s.
(b) $1.00~$s.
(c) $1.50~$s.
(d) $2.00~$s.

Find the time for it to reach its maximum height and also the time taken for it to return to the ground. Sketch the $y$-$t$ graph, $v$-$t$ graph and $a$-$t$ graph for the motion. Assume $g=9.80~$m/s$^2$.

Solution (click to expand)
(a) 6.28m, 10.1m/s
(b) 10.1m, 5.2m/s
(c) 11.5m, 0.3m/s
(d) 10.4m, -4.60m/s

EXAMPLE 2: A ball thrown straight down.

A ball is thrown straight down with an initial velocity of $14.0~$m/s from the edge of a cliff which is 70.0 m above the sea. Calculate the displacement and velocity at times of:

(a) $0.50~$s.
(b) $1.00~$s.
(c) $1.50~$s.
(d) $2.00~$s.
(e) $2.50~$s.

At what time does the ball hit the sea surface? Sketch the $y$-$t$ graph, $v$-$t$ graph and $a$-$t$ graph for the motion. Assume $g=9.80~$m/s$^2$.

Solution (click to expand)
(a) -8.23m, -18.9m/s
(b) -18.9m, 23.8m/s
(c) -32.0m, -28.7m/s
(d) -47.6m, -33.60m/s
(e) -65.6m, -38.5m/s

EXAMPLE 3: Diver motion.

A diver bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of $4.00~$m/s, and her takeoff point is $1.80~$m above the pool.

(a) How long are her feet in the air?
(b) What is her highest point above the board?
(c) What is her velocity when her feet hit the water?

Solution (click to expand)
(a) 1.14s
(b) 0.816m
(c) -7.16m/s

EXAMPLE 4: Throwing a ball upward at edge of cliff.

An object is thrown vertically upwards with an initial velocity of $25~$m/s from the edge of a cliff that is $30~$m from the sea below. Assuming $g=10~$m/s$^2$, determine

(a) the object's maximum height (above the sea).
(b) the time taken for the object to reach its maximum height.
(c) the time taken to reach the surface of the sea.
(d) the speed of the object when it hits the sea.

Solution (click to expand)
(a) 61.3m above sea
(b) 2.5s
(c) 6s
(d) 35m/s

EXAMPLE 5: Ball thrown up past window.

A ball is thrown straight up. It passes a $2.00~$m-high window $7.50~$m off the ground on its path up and takes $1.30~$s to go past the window. What was the ball's initial velocity?

Solution (click to expand)
Ans. 14.5m/s.