Answer:
The baseball will stay 10.47s longer on the moon than on the earth.
Step-by-step explanation:
The amount of time the baseball on the moon will stay in air is until
[tex]h(t)= -0.8t^2+10t+2 =0[/tex]. (i.e when the ball reaches the ground)
Similarly, the amount of time the baseball on earth will stay in air is until
[tex]h(t)-4.9t^2+10t+2=0[/tex]
The solution to these equations can be found using the quadratic formula.
For the baseball on the moon
[tex]-0.8t^2+10t+2 =0[/tex]
[tex]t = \dfrac{-10\pm \sqrt{10^2-4(-0.8*2)} }{2*-0.8}[/tex]
whose positive solution is
[tex]\boxed{t= 12.697s}[/tex]
And for the baseball on earth
[tex]-4.9t^2+10t+2 =0[/tex]
[tex]t = \dfrac{-10\pm \sqrt{10^2-4(-4.9*2)} }{2*-4.9}[/tex]
whose positive solution is
[tex]\boxed{t = 2.224s}[/tex]
Thus, the baseball will stay [tex]12.697s-2.2243s=10.472s[/tex] longer on the moon than on the earth.
