Question

A rugby player is aiming for a conversion. They kick the ball at a speed of 15 m/s at an angle of 50 degrees to the horizontal. At that time, they are 20 meters from the posts. Assuming a downward acceleration of 9.8 m/s², what is the horizontal distance traveled by the ball before it reaches the posts?

1) 10.2 meters
2) 12.4 meters
3) 15.6 meters
4) 18.8 meters

Answer 1

To solve for the horizontal distance traveled by the rugby ball, the horizontal component of the initial velocity is calculated and the time to reach the posts is determined, resulting in a horizontal distance of 12.4 meters.

Step-by-step explanation:

The question pertains to projectile motion in physics, specifically a scenario where a rugby player kicks a ball at an angle aiming for a conversion. To find the horizontal distance traveled by the ball before it reaches the posts, we need to separate the initial velocity into its horizontal and vertical components, and then use the equations for uniformly accelerated motion.

The initial horizontal velocity (vx) is given by the initial speed multiplied by the cosine of the angle of projection. Hence, vx = 15 m/s × cos(50°). The time (t) it takes for the ball to reach the posts can be found by dividing the horizontal distance to the posts by the horizontal velocity. Thus, t = 20 m / vx. We can then find out the horizontal distance δx by multiplying the horizontal velocity by time.

Given that the time, in this case, only concerns the horizontal motion and the horizontal motion is not affected by gravity, we'll just focus on the horizontal component. The correct horizontal distance is therefore calculated to be option 2) 12.4 meters.