Question

A punter in a football game kicks a ball from the goal line at 45 degrees to the horizontal at 20 m/s. How far down the field will the ball land?

Answer 1

The ball will land a distance of 14.14 meters down the field from the goal line.

Step-by-step explanation:

To find how far down the field the ball will land, we can use the horizontal and vertical components of the ball's initial velocity. The horizontal component will determine the distance traveled, and the vertical component will determine the height reached by the ball. In this case, the ball is kicked at an angle of 45 degrees to the horizontal, so the horizontal component of the initial velocity is given by:

horizontal velocity = initial velocity * cos(angle)

Using the given initial velocity of 20 m/s and the angle of 45 degrees, the horizontal component of the velocity is:

horizontal velocity = 20 m/s * cos(45 degrees) = 20 m/s * 0.7071 = 14.14 m/s

The ball will land at the same height as it was kicked from, therefore, the vertical component of the initial velocity is zero. Hence, the ball will land a distance of 14.14 meters down the field from the goal line.