A fighter aircraft is launched from the deck of a...

A fighter aircraft is launched from the deck of a Nimitz-class aircraft carrier with the help of a steam catapult. If the aircraft is to attain a takeoff speed of at least $240 \mathrm{ft} / \mathrm{sec}$ after traveling $800 \mathrm{ft}$ along the flight deck, find the minimum acceleration it must be subjected to, assuming it is constant.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Uniform Acceleration

Uniform acceleration means that an object's acceleration is constant throughout its motion. This concept is essential because it allows for the direct application of kinematic equations, ensuring that the relationships between velocity, displacement, and acceleration are predictable and can be used to determine necessary parameters such as minimum acceleration for takeoff.

Kinematic Equations for Constant Acceleration

These equations, which include formulas such as v² = u² + 2as, relate an object's displacement, initial velocity, final velocity, acceleration, and time under the assumption that acceleration is constant. They are crucial for solving problems where an object (like an aircraft on a carrier deck) accelerates from rest over a known distance to reach a certain speed.

Transcript

00:01 All right, so we want acceleration to be constant, and we're starting an aircraft at zero.

00:08 So let's start here.

00:11 We want a constant acceleration, and we want to go up to a minimum of 240 feet per second.

00:21 And we have 800, let's rewrite that a little bit, 800 feet in which to do that.

00:31 Okay, so we want to figure that out.

00:37 Let's see.

00:39 So acceleration is going to be some constant, and that is going to be the derivative of velocity.

00:50 So then the velocity is going to be the integral of this, some constant t plus another constant d.

00:57 And we want the velocity at this point to be 240.

01:01 Velocity of zero is going to be zero, because we're starting from rest.

01:06 So that actually gives us that d is zero when we put zero into there.

01:10 Okay, so velocity is just c times some time.

01:16 I don't know what the time is yet.

01:17 I don't know how long it takes to go 800 feet.

01:20 So let's keep going.

01:21 Velocity is derivative of displacement.

01:25 So that means displacement is c over 2 t squared plus some other constant e.

01:31 And now i know a few things about displacement.

01:33 I started, let's say, at zero.

01:35 D of zero, is zero, which means that e is zero...

Please give Ace some feedback