Answer:
Maximum altitude: 497.96 ft
Horizontal range: 1007.37 ft
Speed at impact: 165.21 ft/s
Step-by-step explanation:
angle(α) = atan (7/6) = 49.4°
Maximum altitude is given by the formula:
[tex]h=\frac{V_0^2sin^2\alpha }{2g}[/tex]
[tex]h=\frac{100^2 sin^2(49.4)}{2*9.81} =\frac{9770}{19.62}=497.96 ft/s[/tex]
Horizontal range is given by the formula:
[tex]X=\frac{V_0^2sin(2\alpha)}{g}[/tex]
[tex]X=\frac{100^2sin(2*49.4)}{*9.81}=1007.37 ft[/tex]
Speed at impact is given by the formula:
[tex]V_f=\sqrt{V_x^2 + Vy^2}[/tex]
where:
[tex]V_x= V_0cos(\alpha )= 100cos(49.4)=65.07 ft/s[/tex]
[tex]V_y=V_0sin(\alpha ) + gt=100sin(49.4)+9.81(t)[/tex]
[tex]t=\frac{V_0sin(\alpha) }{g}=\frac{100sin(49.4)}{9.81}=7.74s[/tex]
So;
[tex]V_y= 100sin(49.4)+(9.81)(7.74)= 151.86 ft/s[/tex]
[tex]Vf=\sqrt{V_x^2 + V_y^2} =\sqrt{65.07^2+151.86^2}=165.21 ft/s[/tex]
