As stated, the impulse and momentum definitions will be used to later find the value of time through the force of gravity. According to the theory, the impulse formula is given as,
[tex]I = F\Delta t[/tex]
Here,
F = Force
[tex]\Delta t =[/tex] Change in time
Now using the impulse theorem we have that,
Change in Impulse = Change in momentum
[tex]F\Delta t = \Delta p[/tex] (1)
The change in momentum is given as
[tex]\Delta p = p_f -p_i[/tex]
[tex]\Delta p = (-10.6)-(-5.6)[/tex]
[tex]\Delta p = -5m/s[/tex]
The force due to gravity is through the Newton's second law
[tex]F_g = -mg[/tex]
Here,
m = mass
g = Acceleration due to gravity
Substitute the value in (1)
[tex]-mgt = -5m/s[/tex]
[tex]9.8t = 4.9[/tex]
[tex]t = \frac{5}{9.8}[/tex]
[tex]t = 0.51s[/tex]
Therefore it will take 0.51s.
