# Problem: A certain jet comes in for a landing on solid ground with a speed of 100 m/s and its acceleration can have a maximum magnitude of 5.00 m/s2 as it comes to rest. (a) From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest?(b) Can this jet land at a small tropical island airport where the runway is 0.800 km long?

83% (51 ratings)
###### FREE Expert Solution

In this problem, we are required to calculate the time elapsed before a decelerating object comes to rest and the distance covered before stopping given its initial velocity, v0 and the deceleration, -a.

This is a Kinematics problem since it involves initial velocity, v0, acceleration, a, distance covered, Δx, and time, t

We'll follow the following simple steps!

1. Identify the target variable, knowns, and Unknowns for each part of the problem—remember that only 3 of the 5 variables (Δx, v0, vf, a, and t) are needed to solve any kinematics problem.
2. Choose a UAM equation with only one unknown, which should be our target variable.
3. Solve the equation for the target variable, then substitute known values and calculate the answer.

We need to remember the four kinematic equations in order to solve the problem. These are:

$\overline{){{\mathbit{v}}}_{{\mathbit{f}}}{\mathbf{=}}{{\mathbit{v}}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbit{a}}{\mathbit{t}}\phantom{\rule{0ex}{0ex}}{\mathbit{\Delta }}{\mathbit{x}}{\mathbf{=}}{\mathbf{\left(}}\frac{{\mathbit{v}}_{\mathbit{f}}\mathbf{+}{\mathbit{v}}_{\mathbf{0}}}{\mathbf{2}}{\mathbf{\right)}}{\mathbit{t}}\phantom{\rule{0ex}{0ex}}{\mathbit{\Delta }}{\mathbit{x}}{\mathbf{=}}{{\mathbit{v}}}_{{\mathbf{0}}}{\mathbit{t}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbit{a}}{{\mathbit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{{\mathbit{v}}}_{{\mathbit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathbit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbit{a}}{\mathbit{\Delta }}{\mathbit{x}}}$

83% (51 ratings) ###### Problem Details

A certain jet comes in for a landing on solid ground with a speed of 100 m/s and its acceleration can have a maximum magnitude of 5.00 m/s2 as it comes to rest.
(a) From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest?
(b) Can this jet land at a small tropical island airport where the runway is 0.800 km long?