Once it hits the runway, how long till the Jet stops?

[therza7001]

A jet plane lands with a velocity of 101 meters/second and can accelerate at -5.1 meters/second2 when coming to a rest.

a) Once it hits the runway, how long till it stops?

b) Can this plane land on Gilligan’s Island if its runway is 0.80 x 109 μ meters long?



2. Homework Equations

v = v0 + at
x − x0 = (1/2)(v0 + v)t
x = x0 + v0t + (1/2)at^2



3. The Attempt at a Solution

I have no idea how to do this problem. I have had one physics class. Sorry guys. Your help would be great

 

[therza7001]

Sorry guys... i should of labeled the title to be something like..."distance covered with changing velocity" sorry I'm new here

 

[m2003]

.

Hello,

Thank you for reaching out for help with your physics homework. I would be happy to assist you with this problem.

To answer the first question, we can use the equation v = v0 + at, where v is the final velocity (in this case, 0 m/s), v0 is the initial velocity (101 m/s), a is the acceleration (-5.1 m/s^2), and t is the time we are trying to find. We can rearrange this equation to solve for t:

t = (v - v0)/a

Substituting in the values, we get:

t = (0 m/s - 101 m/s)/(-5.1 m/s^2) = 19.8 seconds

Therefore, it will take approximately 19.8 seconds for the plane to come to a complete stop once it hits the runway.

For the second question, we can use the equation x = x0 + v0t + (1/2)at^2, where x is the distance traveled (in this case, 0.80 x 10^9 μ meters), x0 is the initial position (0 meters), v0 is the initial velocity (101 m/s), a is the acceleration (-5.1 m/s^2), and t is the time we found in the first question (19.8 seconds). We can rearrange this equation to solve for v0:

v0 = (x - x0 - (1/2)at^2)/t

Substituting in the values, we get:

v0 = (0.80 x 10^9 μ meters - 0 meters - (1/2)(-5.1 m/s^2)(19.8 seconds)^2)/(19.8 seconds) = 100.5 m/s

Therefore, the initial velocity of the plane must be at least 100.5 m/s for it to be able to land on Gilligan's Island's runway, assuming no other factors (such as air resistance) are involved.

I hope this helps you with your homework. If you have any further questions, please don't hesitate to ask. Good luck!