Calculate the constant acceleration a in g 's which the...

Calculate the constant acceleration $a$ in $g$ 's which the catapult of an aircraft carrier must provide to produce a launch velocity of $180 \mathrm{mi} / \mathrm{hr}$ in a distance of 300 ft. Assume that the carrier is at anchor.

Key Concepts

Constant Acceleration

This concept refers to the motion of an object when its acceleration remains unchanged over time. In projectile motion or launch scenarios, such as in a catapult of an aircraft carrier, understanding constant acceleration is essential because it allows the use of kinematic equations to relate initial velocity, final velocity, acceleration, and displacement.

Kinematic Equations

Kinematic equations are mathematical formulas that describe the motion of objects undergoing constant acceleration. They provide relationships between displacement, initial velocity, final velocity, acceleration, and time, and are crucial in solving problems where one of these variables is unknown, such as calculating the required launch acceleration over a given distance.

Unit Conversion

Unit conversion is the process of converting measurements from one set of units to another, ensuring consistency across calculations. In this context, converting speeds from miles per hour to feet per second and accelerations from feet per second squared to multiples of the acceleration due to gravity is essential for accurately applying the kinematic equations and interpreting the results.

Gravitational Acceleration

Gravitational acceleration, commonly denoted as 'g', is the acceleration due to the Earth's gravity, approximately 32.2 ft/s². Expressing acceleration in terms of g's makes it easier to compare the magnitude of accelerations in different contexts and is particularly useful in applications involving human tolerances and engineering constraints, such as in the design of aircraft carrier catapults.

Transcript

00:01 Okay, a catapult on an aircraft carrier can launch a jet at 180 miles an hour over a distance of 300 feet.

00:20 So we have our velocity and we have our displacement.

00:27 So we need to figure out how many gs on this plane its pilot are going to experience over this distance.

00:34 So to do that first, we're going to convert these to more friendly units.

00:41 We're going to convert our velocity to meters per second and our displacement to meters.

00:48 So let's just multiply this out.

00:52 We have 1 ,609 meters for one mile, and we have 3 ,600 seconds in one hour.

01:07 And this will give us 80 .45 meters per second.

01:17 And for our displacement, one meter is equal to, sorry, i shouldn't put that equal sign now.

01:29 Let's raise that.

01:35 One meter is equal to 3 .28 feet.

01:45 So now calculate this.

01:49 That comes up to 91 .4 .7.

01:53 6 meters.

01:56 So as far as running the acceleration, first we're going to want to know what our average velocity is.

02:01 And the average velocity can be expressed as the average to the final and initial velocity for constant acceleration.

02:17 We do have constant acceleration here.

02:19 So we know that our initial velocity is actually zero.

02:23 So we can ignore this.

02:25 And we're just going to have our final velocity divided by 2, which is 40 .23 meters per second...

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