The time superman will fly before catching the child is 2 seconds.
The distance superman flies to catch the child is 78.4 m.
In any object falling under the influence of the earth’s gravitational force, its motion can be predicted using the three kinematic equations of Newtonian mechanics
Given,
The initial velocity of the child is 0 m/s.
The final velocity of the child is 39.2 m/s.
The superman started traveling, after seconds the child started falling.
The time taken by the child in the fall can be calculated using the first kinematic equation as below,
[tex]\begin{aligned} v&=u+at \\ t&=\frac{v-u}{a} \\ &=\frac{39.2\text{ m/s}-0\text{ m/s}}{9.8\text{ m/}{{\text{s}}^{2}}} \\ &=4\text{ s} \end{aligned}[/tex]
Since superman reacts after 2 seconds when the child starts falling, and he catches the child finally, then he must have traveled (4 s - 2s) that is 2 s.
The distance traveled by the superman must be equal to the distance traveled by the child.
The distance traveled by the child, and hence by superman, in the fall can be calculated using the third kinematic equation as below,
[tex]\begin{aligned} {{v}^{2}}&={{u}^{2}}+2aS \\ S&=\frac{{{v}^{2}}-{{u}^{2}}}{2a} \\ &=\frac{{{\left( 39.2\text{ m/s} \right)}^{2}}-{{\left( 0\text{ m/s} \right)}^{2}}}{2\left( 9.8\text{ m/}{{\text{s}}^{2}} \right)} \\ &=78.4\text{ m} \end{aligned}[/tex]
Thus, the time superman took is 2 seconds and the distance traveled by him is 78.4 meters.
Learn more about the kinematic equation, here:
https://brainly.com/question/12351668
