Harry Potter is chasing his nemesis Draco Malfoy during a Quidditch match. Initially, Harry is 60 meters behind Draco, and at the same moment, the Golden Snitch is 25 meters in front of Draco at the edge of the playing field. Draco flies at a constant speed of 40 m/s straight towards the Golden Snitch. If Harry is originally flying at 50 m/s, what acceleration does he need to reach the Snitch 1.80 meters ahead of Draco? Additionally, how fast will Harry be moving when he passes Draco?

Harry needs an acceleration of approximately 4.80 m/s² to reach the Snitch 1.80 meters ahead of Draco. He will be moving at a speed of approximately 58.5 m/s when he passes Draco.

Explanation:

To calculate the acceleration that Harry needs to reach the Snitch 1.80 meters ahead of Draco, we can use the equation:

a = (vf^2 - vi^2) / (2 * d)

Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and d is the distance. Given that the initial velocity is 50 m/s, the final velocity is the speed needed to reach the Snitch 1.80 meters ahead of Draco, and the distance is the initial distance between Harry and Draco plus the additional distance of 1.80 meters.

By rearranging the equation, we get:

vf = sqrt(2 * a * d + vi^2)

In this case, we have d = 60 m + 1.80 m and vi = 50 m/s. Substituting these values into the equation, we find that the final velocity needed is approximately 58.5 m/s. To find the acceleration required, we can substitute the values into the original equation, which gives us an acceleration of approximately 4.80 m/s².

Therefore, Harry needs an acceleration of approximately 4.80 m/s² to reach the Snitch 1.80 meters ahead of Draco. When he passes Draco, Harry will be moving at a speed of approximately 58.5 m/s.