Question

a window is 50 cm long a stone is thrown from a height of 40 cm above the window find out the time it will take to cross the window

Answer 1

To solve this question you'll apply the equations of motion as follows:

SUVAT-- s-displacement, u-initial velocity, v-final velocity,a- acceleration, t-timev=u + atv2 = u2 + 2ass=1/2(u+v)ts=ut + 1/2at2

The values for the falling stone are as follows:
a= 9.8 m/s2 (is acceleration due to gravity)
u= 0 m/s  (the stone's velocity at the start)
s= 0.5 m  and 0.4 m  (convert 50cm and 40 cm to meters)

lets use the last equation to solve this(pick the one that has the relevant values)    s= ut + 1/2at^2  (since u=0, then ut = 0  ,  hence s= 1/2at^2)

time taken to reach top of the window:
s=1/2at^2
0.4= 1/2 x 9.8 x t^2
0.4= 4.9t^2
t^2=0.4/4.9    t^2=0.0816
                       t= 0.2857
The stone reaches the top of the window after 0.2857 seconds.

Time taken to cross the length of the window:

s=1/2at^2
0.5=1/2 x 9.8 x t^2        0.5= 4.9t^2   t^2=0.5/4.9
                                                           t^2=0.1020
                                                            t=  0.3194
The time the stone crosses the window= 0.3194 seconds

The total time the stone takes from its height until it crosses the window;
0.3194 + 0.2857  =  0.6051 seconds

Answer 2

Given : S1 = 40 cm = 0.4 m
S2 = 50 cm = 0.5 m
S=S1+S2 = 0.4+0.5 = 0.9 m = 9/10 ma = 9.8 m/s2
uinitial = 0 Therefore from 2nd equation of motion ;s= ut+ ½ ×at29/10 = 0×t + ½ × 9.8 × t2 9/10 = 0+4.9×t2t = √9/√49t = 3/7 seconds