Math CentralQuandaries & Queries


Question from Amy:

An egg falls from rest a distance of 75cm to the floor.
Neglecting air resistance, at what speed does it hit the floor?

Hi Amy,

I am going to measure the y-coordinate upwards from the floor and time in seconds. Hence at time $t = 0$ seconds the egg is at $ y = 75$ cm. The displacement $s$ of the egg after $t$ seconds is given by

\[s = s_0 + u t + \frac12 a t^2\]

where $u$ is the initial velocity in cm per second, $s_0$ is the initial displacement of the egg in cm and $a$ is the acceleration due to gravity in cm per second per second. Since positive is upwards $a$ is negative. Since the egg is initially at 75 cm above the floor, $s_0 = 75$ cm.

The egg starts at rest so $u = 0$ cm per second and hits the floor when $s = 0$ cm. Substitute what you know into the equation for $s$ when the egg hits the ground and solve for $t.$

The velocity of the egg starts at zero cm per second and changes at the rate of $a$ cm per second every second. What is the velocity when the egg hits the ground?

I hope this helps,

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