A fully plane has a constant acceleration while moving down a runaway. the plane requires .7 mile of runaway and a speed of 160 miles per hour in order to lift off. what is the planes accelearation?
i need the formula cause the one i have doesnt work cause i need time
vel = at where t is in hrs, and a is in miles/hrs^2
then s = (1/2)at^2 where s is the distance in miles
when v = 160
at=160
t = 160/a
when s= .7
(1/2)a(160/a)^2 = .7
a = 18285.7 miles/hrs^2
so what time is liftoff?
160 = 18285t
t = .00875 hrs or 31.5 seconds
check:
at t= 0,
v = 0
s = 0
when t = .00875
v = 18285.7(.00875) = 160
s = (1/2)(18285.7)(.00875)^2 = .699999
To find the plane's acceleration, we can use the following formula:
v² = u² + 2as
Where:
v = final velocity (speed of lift-off) = 160 miles per hour
u = initial velocity (speed while starting) = 0 miles per hour (plane starts from rest)
a = acceleration (what we need to find)
s = displacement (runway length) = 0.7 miles
First, let's convert the speeds from miles per hour to miles per minute, as it will make the calculations easier.
160 miles per hour = 2.67 miles per minute
0 miles per hour = 0 miles per minute
Now, we can substitute the values into the formula and solve for acceleration:
(2.67 miles per minute)² = (0 miles per minute)² + 2a * (0.7 miles)
7.1289 = 0 + 1.4a
7.1289 = 1.4a
Now, divide both sides of the equation by 1.4:
7.1289 / 1.4 = a
a ≈ 5.0921 miles per minute²
Therefore, the plane's acceleration is approximately 5.0921 miles per minute².