At what angle should an arrow with an initial speed of 45m/s be aimed so that it will hit an apple 25m away on the same horizontal line?

Write the equation for the horizontal position of the arrow as a function of time and its initial velocity and angle, and set it equal to 25 m.. Then write out the equation for vertical motion, also as a function of time and initial velocity and angle, and set it to 0. Now you have two equations in two unknowns (time and angle); solve for the angle.

Write the equation for the horizontal position of the arrow as a function of time and its initial velocity and angle, and set it equal to 25 m.. Then write out the equation for vertical motion, also as a function of time and initial velocity and angle, and set it to 0. Now you have two equations in two unknowns (time and angle); solve for the angle.

sorry I don't get what you are saying. Please can you write down an example equation as a function of time. I really appreciate your kind help.

sorry I don't get what you are saying. Please can you write down an example equation as a function of time. I really appreciate your kind help.

If a projectile is launched at angle \theta from the horizontal with initial velocity v_i, the component of its horizontal velocity is v_x = v_i \cos ( \theta) , and its horizontal position as a function of time is:

x(t) = v_i \cos (\theta) t.

It's initial vertical velocity is v_i \sin (\theta), and its vertical position as a function of time is:

y(t) = v_i \sin (\theta) t - \frac 1 2 g t^2.

I trust these equations are not unfamiliar to you.