Question

An archer uses a bow to fire two similar arrows with the same string force. One

Answer 1

Answer:

answers the correct one is C

Explanation:

For this exercise we must use the projectile launch ratios

the expressions for the initial velocities are

           sin θ =v_{oy} / vo

           cos θ = v₀ₓ / vo

           v_{oy} = v₀ sin θ

           v₀ₓ = v₀ cos θ

Range and flight time are requested

the expression for the scope is

          R = $\frac{ v_{o}^2 \ sin 2 \theta}{g}$

           

We calculate for each angle

θ = 45º

          R₄₅ = \frac{ v_{o}^2 \  sin  90}{g}

          R₄₅ = v₀² / g

 

θ = 60º

          R₆₀ = \frac{ v_{o}^2 \  sin  120}{g}

          sin  120 = sin 60

          R₆₀60 = sin  60  R₄₅

as the sine function has values ​​between 0 and 1, the range for this angle is less

Flight time is twice the time it takes to reach maximum altitude

           v_y = v_{oy} - gt

at the point of maximum height there is no vertical velocity vy = 0

           t = v_{oy} / g

           t = v₀ sin θ / g

θ=45º angle

           t₄₅ = sin 45  v₀/g

           t₄₅ = 0.707 v₀/g

θ=60º angle

          t₆₀ = sin 60 v₀/ g

          t₆₀ = 0.86   v₀/g

         

 

the answer for this part is

           R₄₅ > R₆₀

            t₄₅ < t₆₀

when reviewing the different answers the correct one is C