Answer:
Ranking:
326.4 m, 312.4 m, 186 m, 140.5 m, 86.6 m, 27.9 m
Explanation:
Projectile Motion
It's known as the type of motion that experiences an object that is launched near the Earth's surface and moves along a curved path exclusively under the action of gravity.
Being vo the initial speed of the object, θ the initial launch angle, and g=9.8m/s^2 the acceleration of gravity, then the maximum vertical height the object reaches is calculated by:
[tex]\displaystyle h_m=\frac{v_o^2\sin^2\theta}{2g}[/tex]
We have to test for different launching angles and sort the maximum heights from lowest to highest. For all the test cases, vo=80 m/s.
[tex]\displaystyle h_m=\frac{80^2\sin^2 31^\circ}{2\cdot 9.8}[/tex]
h=86.6 m
[tex]\displaystyle h_m=\frac{80^2\sin^2 89^\circ}{2\cdot 9.8}[/tex]
h=326.4 m
[tex]\displaystyle h_m=\frac{80^2\sin^2 17^\circ}{2\cdot 9.8}[/tex]
h=27.9 m
[tex]\displaystyle h_m=\frac{80^2\sin^2 49^\circ}{2\cdot 9.8}[/tex]
h=186 m
[tex]\displaystyle h_m=\frac{80^2\sin^2 41^\circ}{2\cdot 9.8}[/tex]
h=140.5 m
[tex]\displaystyle h_m=\frac{80^2\sin^2 78^\circ}{2\cdot 9.8}[/tex]
h=312.4 m
Ranking:
326.4 m, 312.4 m, 186 m, 140.5 m, 86.6 m, 27.9 m
