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AlexJicu08

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Thread moved from the technical forums to the schoolwork forums

Recently I started making physics problems and I made one that I really like, but I would like some feedback from other people (how difficult it is, how enjoyable it is to solve this problem, what I could improve about it, etc). Here is the problem:

A cannon is fixed at height H relative to the Earth in point A. The length of the cannon is l, and it can rotate around point O, making an angle φ with the horizontal axis.

A sphere-shaped projectile of radius R and density ρ leaves the cannon with speed v0 under the same angle φ. Friction with air has the value Fr = λρ0Sv^2, where S is the cross-section area of the sphere, v is its velocity, λ is a coefficient and ρ0 is the density of air. This force acts opposite to the velocity. The air also acts on the projectile with a buoyant force equal to the weight of the air displaced by the object.

a) Determine the SI unit for λ

b) Express the horizontal distance relative to point O at which the projectile gets as a function of l, H, φ, λ, ρ, ρ0, R, v0 and g

c) Calculate the distance d for φ ∈ {0°; 30°; 45°; 60°; 90°} (g=10m/s^2, H=2m, l=1m, v0=18km/h, ρ0=1.29kg/m^3, ρ=0.5g/cm^3, R=0.5m and λ = 1 (SI units)

d) Graph d as a function of φ evidentiating the values calculated at point c) and determine, from the graph, for what angle is d maximum

A cannon is fixed at height H relative to the Earth in point A. The length of the cannon is l, and it can rotate around point O, making an angle φ with the horizontal axis.

A sphere-shaped projectile of radius R and density ρ leaves the cannon with speed v0 under the same angle φ. Friction with air has the value Fr = λρ0Sv^2, where S is the cross-section area of the sphere, v is its velocity, λ is a coefficient and ρ0 is the density of air. This force acts opposite to the velocity. The air also acts on the projectile with a buoyant force equal to the weight of the air displaced by the object.

a) Determine the SI unit for λ

b) Express the horizontal distance relative to point O at which the projectile gets as a function of l, H, φ, λ, ρ, ρ0, R, v0 and g

c) Calculate the distance d for φ ∈ {0°; 30°; 45°; 60°; 90°} (g=10m/s^2, H=2m, l=1m, v0=18km/h, ρ0=1.29kg/m^3, ρ=0.5g/cm^3, R=0.5m and λ = 1 (SI units)

d) Graph d as a function of φ evidentiating the values calculated at point c) and determine, from the graph, for what angle is d maximum

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