Answer:
[tex]t=1.020s[/tex]
Step-by-step explanation:
Given Equation:
[tex]5t-0.5at^{2} =0[/tex]
Actually the given equation is the 2nd equation of motion
i.e. [tex]S =V_{i} t+0.5at^{2}[/tex]
where [tex]S=0[/tex] because the astronaut jumps on the earth
and initial velocity [tex]V_{i}=5[/tex]
to find time [tex]t[/tex], put the given value of [tex]a=9.8m/s^{2}[/tex] in the given equation, we get
[tex]5t-0.5(9.8)t^{2} =0\\t(5-4.9t)=0\\ \ dividing\ both\ sides\ by\ t\ we \ get\\ 5-4.9t=0\\4.9t=5\\t=\frac{5}{4.9}\\ t=1.020s[/tex]
it will take [tex]t=1.020s[/tex] to reach the ground if he jumps on the Earth
