You fire an arrow at an angle of 45o from the horizontal and it lands a distance of 100 m from you. if you fire an identical arrow at the same speed but at 46o, how far away from you will it land? ignore air resistance.

Arrow projected at an angle of 46⁰ will travel 99.94 m.

Explanation:

   The arrow fired at an angle 45⁰ travels 100 m horizontally, the horizontal movement is because of horizontal component of velocity.

   Horizontal component = u cos θ, where u is the velocity of projection.

   The time taken to travel 100m is depending on vertical component of velocity, time taken is calculated by dividing vertical component of velocity by acceleration due to gravity and multiplying by two.

    So, time taken = 2u sin θ/g

    Horizontal distance travelled by projectile,

    So. H ∝ sin 2θ

      Here  

 So an arrow projected at an angle of 46⁰ will travel 99.94 m.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west