Answer:
The mountain is 403 m tall
Explanation:
Horizontal Launch
When an object is thrown horizontally with a speed v from a height h, it describes a curved path ruled by gravity until it hits the ground.
The range or maximum horizontal distance traveled by the object can be calculated as follows:
[tex]\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}[/tex]
It's given that if a ball is kicked from the top of the Sugarloaf Mountain, it will land near its base without hitting the side. The initial speed is v=9.37 m/s and it reaches a horizontal distance of d=85 m. Solving the equation for h:
[tex]\displaystyle h=\frac{d^2g}{2v^2}[/tex]
Substituting:
[tex]\displaystyle h=\frac{85^2*9.8}{2*9.37^2}[/tex]
[tex]\displaystyle h=403 \ m[/tex]
The mountain is 403 m tall
