Answer: 31.6 m
Explanation:
This situation is a good example of the projectile motion or parabolic motion, in which the travel of the stone has two components: x-component and y-component. Being their main equations as follows:
x-component:
[tex]x=V_{o}cos\theta t[/tex] (1)
Where:
[tex]V_{o}=7.5m/s[/tex] is the stone's initial speed
[tex]\theta=0[/tex] because we are told the stone is thrown horizontally
[tex]t[/tex] is the time since the stone is thrown until it hits the ground
y-component:
[tex]y=y_{o}+V_{o}sin\theta t+\frac{gt^{2}}{2}[/tex] (2)
Where:
[tex]y_{o}=87 m[/tex] is the initial height of the stone
[tex]y=0[/tex] is the final height of the stone (when it finally hits the ground)
[tex]g=-9.8m/s^{2}[/tex] is the acceleration due gravity
Finding [tex]t[/tex] from (2):
[tex]0=y_{o}+\frac{gt^{2}}{2}[/tex] (3)
[tex]t=\sqrt{\frac{-2y_{o}}{g}}[/tex] (4)
Substituting (4) in (1):
[tex]x=V_{o}cos(0\°) \sqrt{\frac{-2y_{o}}{g}}[/tex] (5)
[tex]x=V_{o}\sqrt{\frac{-2y_{o}}{g}}[/tex]
[tex]x=7.5 m/s \sqrt{\frac{-2(87 m)}{-9.8m/s^{2}}}[/tex] (6)
Finally:
[tex]x=31.6 m[/tex]
