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 the time, they are 20 m from the posts. How high will the ball be when it reaches the posts?

Answer 1

To find the height of the ball when it reaches the posts, we need to analyze the vertical motion of the ball. By using the horizontal motion formula and the formula for vertical motion, we can calculate that the height of the ball when it reaches the posts is 13.034 meters.

Step-by-step explanation:

To find the height of the ball when it reaches the posts, we can analyze the vertical motion of the ball. We know the initial vertical velocity, which is the vertical component of the ball's initial speed, and the time it takes for the ball to reach the posts, which we can calculate using the horizontal motion of the ball.

Step 1: Calculate the time it takes for the ball to reach the posts. We can use the horizontal motion formula: distance = speed x time. The distance is 20 m and the speed is 15 m/s. Rearranging the formula, we have time = distance / speed, which gives us time = 20 m / 15 m/s = 1.33 s.

Step 2: Calculate the vertical motion of the ball. We know the initial vertical velocity, which is the vertical component of the ball's initial speed. We can use the formula: final vertical velocity = initial vertical velocity + (acceleration x time). In this case, the acceleration is the acceleration due to gravity, which is approximately -9.8 m/s², and the time is 1.33 s. Rearranging the formula, we have initial vertical velocity = (final vertical velocity - (acceleration x time)). Since the ball reaches the posts at the same height it was kicked, the final vertical velocity is 0 m/s. Plugging in the values, we get initial vertical velocity = 0 m/s - (-9.8 m/s²) x 1.33 s = 0 m/s + 13.034 m/s = 13.034 m/s.

So, the height of the ball when it reaches the posts is 13.034 meters.