Troubleshooting Homework Problems - Balls, Cliffs & Falling Objects

[lynaa]

Homework Statement

While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

The answer I get is supposed to be 4 cubits

2. Homework Equations
d = 1/2 a t^2

The Attempt at a Solution

Ball is rolling at 1 cubit / 10 count.

t = 20 count = two 10counts = 2t

d = 1/2 a t^2
d = 1/2 a (2t)^2
d = 1/2 * 4t^2 * a
2d = 4t^2 * a
I don't know where to go from here

Homework Statement

Someone standing at the edge of a cliff (as in the following figure) throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below?

This time I do not know what the correct answer will be

Homework Equations

None, theory problem

The Attempt at a Solution

I think that the ball thrown up will have a greater acceleration because it will fall from a higher point (once it reaches that highest point). So it will have a longer time to accelerate.

Homework Statement

A freely falling object falls 5.0s after it is released from a position of rest. How far will it fall in this time?

Express your answer to two significant figures and include the appropriate units.

Homework Equations

d = 1/2 a t^2

The Attempt at a Solution

a = g = -10m/s^2
t = 5s

d = 1/2 (-10m/s^2) (5s)^2
d = -5m/s^2 (25s^2)
d = -125m
want distance fallen so take absolute value of d = -125
d = 125m

But it tells me that I am wrong. :(

 

[RUber]

for the first problem $1/2 a$ is constant in both instances. You have all the information needed to make a comparison.

 

[RUber]

For the second problem, ask yourself how fast will the ball that was thrown upward be traveling when it gets back to the man who threw it. What is that velocity relative to the velocity he threw the downward ball?

 

[RUber]

For the third problem, I suspect there are some rounding errors since it is asking for two significant digits.
Gravity is 9.8m/sec/sec, so there is one possible source of error.

 

[lynaa]

for the first problem $1/2 a$ is constant in both instances. You have all the information needed to make a comparison.

Because they are constant that means that I can I just set it to 1 and ignore it right? I can see how to solve it based on that, but why is it constant? Why am I able to just say it's equal to whatever when solving the problem?

For the second problem, ask yourself how fast will the ball that was thrown upward be traveling when it gets back to the man who threw it. What is that velocity relative to the velocity he threw the downward ball?

Oh, it would be the same velocity as when he threw it up right? So that means that it will be the same thing right?

For the third problem, I suspect there are some rounding errors since it is asking for two significant digits.
Gravity is 9.8m/sec/sec, so there is one possible source of error.

We were told to use 10m/s^2 for everything in gravity. It is only an introductory physics course, so my professor said on the first day to not worry about using 9.8 as it is easier to learn to the concepts with 10m/s^2. Is there another spot that I made an error in?

Also thank you for helping me!

 

[NascentOxygen]

In 1. you could determine your value for a where a is the acceleration directed along the slope due to a component of gravity. Then use that same value for your 2t calculations.

What is 125 expressed to 2 significant figures?

 

[Faris Shajahan]

3rd question

What is the answer given?