In 1780, in what is now referred to as "Brady's Leap,"...

In $1780,$ in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt $22 \mathrm{ft}$ across while falling $20 \mathrm{ft} .$ Tall tale, or possible? a. What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? b. The world-record time for the $100 \mathrm{m}$ dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?

In $1780,$ in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt $22 \mathrm{ft}$ across while falling
$20 \mathrm{ft} .$ Tall tale, or possible?
a. What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river?
b. The world-record time for the $100 \mathrm{m}$ dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?

Key Concepts

Horizontal Velocity

Horizontal velocity in projectile motion is the constant speed at which the object travels along the horizontal axis, independent of simultaneously occurring vertical motion. By knowing the time of fall (determined from free fall calculations), one can calculate the necessary horizontal speed to cover a required distance, such as clearing a gap or river, using the formula horizontal distance = horizontal velocity × time.

Human Running Speed Comparison

Comparing the required horizontal speed to human running speeds is an application of biomechanics and athletic performance metrics. By contrasting the minimum needed speed with known human sprint speeds—such as those observed in world-record events—the reasonableness of achieving the required speed through human effort can be evaluated. This concept contextualizes the physical feasibility of feats described in historical accounts like Brady's leap.

Projectile Motion

Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. This concept is used to analyze movements where horizontal and vertical components of motion are treated independently, allowing one to determine how long an object stays in the air and how far it travels horizontally given its initial velocity.

Free Fall

Free fall refers to the motion of an object where gravity is the only force acting on it. In kinematic calculations, the distance an object falls can be related to the time of fall using the equation s = ½gt². This allows one to compute the time it takes for an object to descend a given vertical distance, which is critical for determining the duration of the airborne phase in projectile motion.

Transcript

00:01 So you're given an x value of 22 feet across and 20 feet down.

00:06 You're asked, is it possible he could have run fast enough to make the problem happen? the first thing you're going to do is convert this to meters.

00:16 0 .3048 meters per foot.

00:20 So you're going to do that for both of these.

00:22 The feet cancel.

00:23 If you do that ratio, 0 .3048 meters per foot and multiply.

00:30 So for the x value, you get 6 .7 meters.

00:41 And for the y value, you get 0 .6 or 6 .1 meters.

00:50 So how fast would you have to run to make it off of the cliff? so for part a, since he runs off horizontally, we know that v, i, y equals zero.

01:02 And so i'm going to look at the vertical part first.

01:05 We know that a is negative 9 .8.

01:09 We know is going to go down a value y of negative 6 .1 meters.

01:14 So how much time should that take? so i'm going to use the equation, y equals v -i -y times t plus 1 -5 -a -t -squared and solve that for time.

01:29 V -i -y is zero.