It is your parent's 25th Wedding Anniversary and you thought it would be special to throw them a surprise party. Your entire family is up north at your Traverse City cottage (240 miles from your home) and you plan on waking up early Saturday morning to drive home and set up for the party. You wake up at 10:00 am to head out but to your surprise your parents decide on leaving at 11:00 am instead of 1:00 pm like they originally planned. Your father ALWAYS drives 60 miles per hour on the expressway and it will take you about 2 hours to set up for the party. How fast must you drive in order to get home in enough time to make the surprise a success? Show your work.

120 miles per hour.

Explanation:

We need to find the time it takes my parents to drive home from the cottage. Since my father drives at 60 miles per hour, and the cottage is 240 miles from our home, and distance = speed × time. So, time = distance/speed = 240 mi/60 mi/h = 4 h.

So, it will take my father 4 hours to drive home from the cottage.

Since I have 2 hours to prepare for the party, the time left for me to drive to the cottage is 4 - 2 hrs = 2 hrs.

So, I'm supposed to drive to the cottage in at most 2 hours.

The speed at which I must drive in this time period is thus,  speed = distance/time = 240 miles/2 hours = 120 miles per hour.

So, I must drive at a minimum speed of 120 miles per hour.

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.