Answer:22.62 m/s
Explanation:
Given
two balls are separated by a distance of 50 m
Alex throws the ball from a height of 50 m with a velocity of 8 m/s and Gary launches a ball with some velocity exactly at the same time.
ball from ground travels a distance of 25 m in t sec
For Person on tree
[tex]25=ut+\frac{1}{2}gt^2[/tex]
[tex]25=8t+\frac{1}{2}\times 9.81\times t^2--------1[/tex]
For person at ground
[tex]23.5=ut-\frac{1}{2}gt^2---------2[/tex]
Solve equation (1)
[tex]50=16t+9.81t^2[/tex]
[tex]9.81t^2+16t-50=0[/tex]
[tex]t=\frac{-16\pm\sqrt{256+4\times 50\times 9.81}}{2\times 9.81}=\frac{47.1-16}{19.62}=1.58 s[/tex]
put the value of t in equation 2
[tex]23.5=u\times 1.58-\frac{9.81\times 1.58^2}{2}[/tex]
[tex]u=\frac{35.744}{1.58}=22.62 m/s[/tex]
