An airplane with a velocity of 50m/s comes in to land at the start of the runway and brakes at -5m/s. Will it be able to stop in time if the runway is 275m long?
I'm not sure which formula to use since the ones I have used give me very small answers in comparison to the 275m
To determine if the airplane will be able to stop in time, we can use the equation for motion under constant acceleration:
\[v^2 = u^2 + 2as\]
Where:
- \(v\) is the final velocity of the airplane (0 m/s since it comes to a stop)
- \(u\) is the initial velocity of the airplane (50 m/s)
- \(a\) is the deceleration of the airplane (-5 m/s^2, since it's braking)
- \(s\) is the distance traveled by the airplane (275 m)
Rearranging the equation, we get:
\[s = \frac{{v^2 - u^2}}{{2a}}\]
Substituting the given values into the equation, we can solve for \(s\):
\[s = \frac{{(0^2) - (50^2)}}{{2(-5)}}\]
\[s = \frac{{0 - 2500}}{{-10}}\]
\[s = \frac{{2500}}{{10}}\]
\[s = 250\]
The calculated distance \(s\) comes out as 250m. Since the calculated distance is less than the actual runway length of 275m, the airplane will be able to stop in time.