Physics Puzzle #9 Mystery Cache

This is the ninth and final puzzle of a series of puzzles based on Kinematics or the study of motion.

I was going to stop at 8 puzzles but I realized that I had an extra hiding spot picked out already with a container already hidden!

Congratulations to denjoa for FTF honours.

This series of caches is reaching the end of its run.

I will be archiving them in August 2022

It is recommended, but not necessary, that you complete the puzzles in order as each puzzle will have an increasing level of difficulty. The puzzles in the series are

Physics Puzzle #1 (GC6XBGC)

Physics Puzzle #2 (GC6XDN0)

Physics Puzzle #3 (GC6XDXM)

Physics Puzzle #4 (GC6XK5Q)

Physics Puzzle #5 (GC6XMW4)

Physics Puzzle #6 (GC6XP3J)

Physics Puzzle #7 (GC6XXY3)

Physics Puzzle #8 (GC6XY1H)

Physics Puzzle #9 (GC6XY50)

The Lesson

An experiment was conducted on the surface of the moon (and yes humans went to the moon) where they dropped a hammer and a feather at the same time and they both struck the ground at the same time. Done on the Earth's surface, we wouldn't get the same results because the moon doesn't have any air to slow down falling objects. Why does air make a difference? Gravity is a force that pulls objects towards the centre of the Earth and air resistance provides a force that opposes the motion of the object. Remove the air and you remove the air resistance. So, if we ignore air resistance, the problems are a lot easier and we can treat everything as though it is falling at 9.8 m/s². From the units, you should be able to tell that this is an acceleration. With this information, we can look at freefall problems as though they are simple kinematics problems where we always know the acceleration.

Example: A baseball is thrown vertically downward from the top of a 155 m tower with an initial velocity of 25 m/s. What is its velocity as it reaches the ground?

Notice the use of the word velocity in the example? With gravity, direction becomes important. If you throw something downward, it will pick up speed. If you throw something upwards, it will slow to a stop and then fall back down. Unlike the cartoons, when something experiences acceleration due to gravity, it starts right away!

The positive for the acceleration means that the baseball is speeding up.

The baseball is going 60.5 m/s when it reaches the ground. Obviously, after reaching the ground the ball is going to bounce and eventually come to a stop. We are only concerned with the instant that it first touches.

In previous puzzles, you didn't have to select the formula. In this puzzle, you are going to have to decide which of the four acceleration formulas you are going to need. I identify the variables first. I was given v₁, d, a, and I was asked for v₂ so I looked for a formula that had those four. Back in puzzle #1, you were identifying quantities in a problem. Now, you have to use that skill.

There are a few quantities that you can surmise...

For an object that is dropped v₁ = 0

For an object that is thrown upwards v₂ = 0 at the maximum height (before dropping back to Earth)

For an object in freefall near the Earth's surface, a = 9.8 m/s² [down]. It will be positive for objects moving downward and negative for objects moving upwards.

A helicopter is ascending vertically with a speed of 8.0 m/s; at a height of 120 m above the earth, a package is dropped from a window. How much time does it take for the package to reach the ground?

A lot of people have trouble picturing this problem because passengers in the helicopter would see the package immediately falling away. In actual fact, the package continues to rise as it stops and then starts to fall downward. A very observant observer who is stationary would be able to see the package continue to rise. That gives the problem two distinct parts: going up and coming down.

The package continues to rise for 0.816 s and rises 3.27 m from the release point as it stops. Coming down, the package falls 123.27 m (120m + 3.27m)

While falling, the package takes a further 5.02 s to reach the ground. The total time in the air was 0.816+5.02 = 5.836 s

A related but easier situation occurs when an object is thrown upwards and it returns to THE SAME HEIGHT. If you calculate the time going up and the time coming back down, you would find that they are the same. Instead of calculating both, you can calculate the time going up OR the time coming down and double it. Again, that is only true if it returns to the same height. For example, a ball is thrown from a height of 2 m above the ground and it is caught at a height of 2 m above the ground.

To save you looking back at the other puzzles, here are all five of the formulas (The plural is actually "formulae") for Kinematics

The Puzzle

Read each of the following problems and solve as indicated. Enter the values in the space provided. Remember: Don't round off until you get to the final answer!

A baseball is thrown vertically with an initial velocity of 32.0 m/s[up]. Find the maximum height reached by the ball. Round to one decimal place.

___ ___.___ (A B.C)

A projectile leaves a pellet gun with a speed of 150 m/s. How long will it be in the air if the gun is fired straight up? Assume that it leaves from ground level and returns to ground level. Round to two decimal places.

___ ___ .___ ___ (D E.F G)

A rock is dropped from the top of a cliff. It is seen to hit the water below after 3.18 s. How high is the cliff? Round to one decimal place.

___ ___ .___ (H J K)

A = __ B = __ C = __ D = __ E = __ F = __ G = __ H = __ J = __ K = __

The cache can be found at N 44° a b.c d e’ and W 078° f g.h j k’

There is no connection between the upper case letters above and the lower case letters here.

a = A - D: _____; b = B^C + G: _____; c = √(J): _____;

d = F + C^E: _____; e = E^J: _____; f = F - D: _____;

g = J^G: _____; h = H^B ÷ C: _____.

j = A^{(D - B)}: _____; k = F ÷ C: _____.

The cache is at: N 44° __ __ . __ __ __ ' and W 078° __ __ . __ __ __'

You can check your answers for this puzzle on GeoChecker.com.