Question

A plane landing on a small tropical island has
just 50 m of runway on which to stop.
If its initial speed is 47 m/s, what is the
maximum acceleration of the plane during
landing, assuming it to be constant?
Answer in units of m/s
2
.

Answer 1

Vi = 47 m/s
d = 50
===============
v = Vi + a t
0 = 47 + a t
a t = -47
or
a = -47/t
===============
d = Vi t + .5 a t^2
50 = 47 t + .5 a t^2
50 = 47 t +.5(-47/t)t^2
50 = 47 t - .5*47 t
50 = .5*47 t
t = 100/47
then
a = -47/(100/47)= -22 m/s^2
> twice gravity
I think maybe 500 meters, not 50

Answer 2

The method above is correct but
The 0.5 is magically gone on the t equation
The t should of been t = 100/23.5