The path of a projectile fired at an inclination (in degrees) to ...

[gbarreiro]

Solve the problem.

The path of a projectile fired at an inclination θ (in degrees) to the horizontal with an initial speed v₀ is a parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by using the formula
R = sin(2θ)
where g is the acceleration due to gravity. The maximum height H of the projectile is
H = (1 - cos(2θ))
Find the range R and the maximum height H in terms of g if the projectile is fired with an initial speed of 200 meters per second at an angle of 15° and then at an angle of 22.5°. Do not use a calculator, but simplify the answers.

[nickk12214]

θ = 15°:  R = ,  H = ;
θ = 22.5°:  R = ,  H =

[rl]

Solve the problem.

The path of a projectile fired at an inclination θ (in degrees) to the horizontal with an initial speed v₀ is a parabola. The maximum height H of the projectile is given by
H = (1 - cos (2θ))
where g is the acceleration due to gravity.
Show that the maximum height H can be written H =

[Swizqar]

H = (1 - cos(2θ)) =   (1 - (1 - 2 sin² θ)) = (2 sin² θ) =