Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground. you have determined that the football would travel 15.1 m before landing. how would this value change if the football was kicked at an angle of 35.0°? complete all equations without rounding and then round to the nearest tenth at the end.

If the football is kicked at a 35.0º angle, it will travel 18.5 m before landing. This is farther than if it were kicked at a 25° angle.

The horizontal distance traveled by the ball (range of motion) is given by the following equation:



In which  is the range of motion,  is the horizontal component of the initial velocity, and  is the time of motion.

First, lets calculate the horizontal component of the initial velocity:



Now, we calculate the time of motion from the equation that described the motion of the ball in the vertical axis:



In which  is the position of the ball vertically,  is the vertical component of the initial velocity,  is the acceleration in the vertical axis (which is gravity), and  is time of motion.

We want to find the time when the ball lands, hence, when ; so the equation becomes:



We rewrite it a bit more:



This is a quadratic equation, so we use the quadratic equation formula to solve for time (we'll get two answers):



Clearly, one of the answers is , this is before you kick the ball (it is on the ground), we want the nonzero answer (when it lands) so:



Now, we plug-in the time value to the equation of the motion's range:



The ball will travel 18.57 meters.