Question

A player kicks up a ball at an angle θ with the horizontal. The horizontal range is maximum when θ is equal to​

Answer 1

Answer:

The horizontal range is maximum when θ is equal to 45°

Explanation:

Projectile Motion

It's known as the type of motion that experiences an object that is projected near the Earth's surface and moves along a curved path exclusively under the action of gravity.

Being vo the initial speed of the object, θ the initial launch angle, and $g=9.8\ m/s^2$ the acceleration of gravity, then the maximum horizontal distance traveled by the object (also called Range) is:

$\displaystyle d={\frac {v_o^{2}\sin(2\theta )}{g}}$

Since the sine of an angle is bounded between -1 and 1, the maximum range will occur when the sine is 1:

$\sin(2\theta)=1$

The only angle between 0° and 360° whose sine is 1 is 90°, thus:

$2\theta=90^\circ$

Solving:

$\theta=45^\circ$

The horizontal range is maximum when θ is equal to 45°