AAMC self assessment #22 Physics

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AAMC Physics Self Assessment #22
Need help with this question please. I thought decreasing g would decrease the time? How do you derive the appropriate formula for this question?

Q: Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in time t. If the value of g were reduced to g/6 (as on the moon) then t would:

Answer
A: increase by a factor of 6

I see how you derive this from v = vo + at, but I used x = 1/2at^2 and got that t increases by sqrt(6), which was an answer choice and wrong. why do I use the first formula?? thanks

 

[Temperature101]

AAMC Physics Self Assessment #22
Need help with this question please. I thought decreasing g would decrease the time? How do you derive the appropriate formula for this question?

Q: Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in time t. If the value of g were reduced to g/6 (as on the moon) then t would:

Answer
A: increase by a factor of 6

I see how you derive this from v = vo + at, but I used x = 1/2at^2 and got that t increases by sqrt(6), which was an answer choice and wrong. why do I use the first formula?? thanks

They are telling you that the ball have an initial velocity, which is v and a final velocity that is zero... If you use x = 1/2 at^2, you are saying that the initial velocity is zero, which is not correct. Remember that the formula you are using is x = VoT + 1/2aT^2 and since Vo is not equal to zero, you cannot use x = 1/2at^2. That is my take on it... May be someone else has another explanation.

 

[eschrodinger]

See Ibn MD explanation.

 

[HotHamH2O]

I would just use ratios to solve it.

Let's split it up into two trials. Trial A and Trial B. We will make Trial A be g and Trial B 1/6g

tB/tA = [1/(1/6g)] / (1/g)

tB = 6tA

 

[Postictal Raiden]

The way I would approach this problem, and I think it is the easiest way, is to figure out the relationship between acceleration due to gravity and time. This is given by the following equation:

g = v/t

Now, we can see that they are inversely proportional, so decreasing one by a factor of x would increase the other by the same factor.

 

[HotHamH2O]

The way I would approach this problem, and I think it is the easiest way, is to figure out the relationship between acceleration due to gravity and time. This is given by the following equation:

g = v/t

Now, we can see that they are inversely proportional, so decreasing one by a factor of x would increase the other by the same factor.

yea...that's much better. And I thought my way was easy lol

 

[Endure]

Good lord. Some of these explanations are some of the most convoluted I've seen on these boards!

AAMC Physics Self Assessment #22
Need help with this question please. I thought decreasing g would decrease the time? How do you derive the appropriate formula for this question?

Q: Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in time t. If the value of g were reduced to g/6 (as on the moon) then t would:

Answer
A: increase by a factor of 6

I see how you derive this from v = vo + at, but I used x = 1/2at^2 and got that t increases by sqrt(6), which was an answer choice and wrong. why do I use the first formula?? thanks

They're telling you that the ball was thrown with an initial velocity, v, and that Δy = 0 (since the ball is returning to its original height).

Δy = v(t) - (1/2)gt^2
0 = v(t) - (1/2)gt^2
v(t) = (1/2)gt^2
v = (1/2)gt

Therefore, t = 2v/g (earth). If g is reduced by a factor of 6, you end up with the following:

t (moon) = 2v/(g/6)
t (moon) = 6 t (earth)

Hope that helps.

 

[DrDashInd]

I would just think about it conceptually. Time to go up is the same as the time to come down. When doing up gravity acts to slow you down to vf = 0 m/s, so when gravity is reduced it takes longer to slow down. Thus increased time of flight.

vf = vo +a*t
0 = vo +(g/6)t
t=vo/(g/6)
thus time is 6 times longer than it would be if g=g.

Also don't forget the units of g. Don't forget the... G-Unit.

 

[Yessi211]

The way I would approach this problem, and I think it is the easiest way, is to figure out the relationship between acceleration due to gravity and time. This is given by the following equation:

g = v/t

Now, we can see that they are inversely proportional, so decreasing one by a factor of x would increase the other by the same factor.

Way I would approach this as well.