An archer uses a bow to fire two similar arrows with the same string force. One arrow is fired at an angle of 60° with the horizontal, and the other is fired at an

angle of 45° with the horizontal. Compared to the arrow fired at 60°, the arrow fired

at 45° has a -

A) longer flight time and longer horizontal range

B) longer flight time and shorter horizontal range

C) shorter flight time and longer horizontal range

D) shorter flight time and shorter horizontal range

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 =

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

a 2,000 calorie based diet.