Answer:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]
Explanation:
To solve this problem, we can use the following suvat equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]
where
[tex]\Delta x[/tex] is the vertical displacement of the frog
[tex]v_0[/tex] is the initial vertical velocity
t is the time
a is the acceleration
We have chosen this formula because apart from [tex]v_0[/tex], all the other quantities are known. In fact:
[tex]\Delta x =0.1 m[/tex] is the vertical displacement
t = 2 s is the total time of flight
[tex]a=g=-9.8 m/s^2[/tex] is the acceleration due to gravity (negative because it is downward)
Therefore, solving for [tex]v_0[/tex], we find the initial velocity of the frog:
[tex]v_0 = \frac{\Delta x-\frac{1}{2}at^2}{t}=\frac{0.1-\frac{1}{2}(-9.8)(2)^2}{2}=9.85 m/s[/tex]
