Velocity question

[callummcgurr]

If anybody could help with this question it would be greatly appreciated.

 

[Deleted member 4993]

If anybody could help with this question it would be greatly appreciated.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[callummcgurr]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

View attachment 31005

Hello, i have crossed out the answers. I know the answers but have no idea on how to get to the answer. I dont even know where to start so any idea how to start solving this problem would be great, thanks.

 

[blamocur]

Hello, i have crossed out the answers. I know the answers but have no idea on how to get to the answer. I dont even know where to start so any idea how to start solving this problem would be great, thanks.

Start by figuring out the values of [imath]s[/imath], then of [imath]t[/imath] when the ball hits the ground.

 

[Deleted member 4993]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

View attachment 31005

You are given an expression for "distance" travelled as a function of time.

What is the relationship between that function and "speed"?

 

[Dr.Peterson]

Hello, i have crossed out the answers. I know the answers but have no idea on how to get to the answer. I dont even know where to start so any idea how to start solving this problem would be great, thanks.

Presumably (a) is asking for the initial speed of the ball, which you are told is 54 km/h. So you just need to convert that to m/s. Do you know any ways to do that?

 

[skeeter]

This is a very poorly posed problem of projectile motion in the vertical direction.

First, the given equation should be [imath]s = u_0 t - \dfrac{1}{2}gt^2[/imath]
where [imath]s[/imath] is displacement (a vector quantity) of the ball from its initial position, not distance.
The value [imath]g =9.8 \, m/s^2[/imath] is the magnitude of the acceleration due to gravity near the Earth’s surface. A negative sign is necessary to indicate its direction since it is also a vector quantity.

Second, you are given the ball’s initial speed, not its velocity, Is the ball initially thrown upward or downward? That important piece of information is not stated.

Part (b) gives the position of the ball as 1/4 of the building’s height measured from the ground, or 39 meters.
That means the ball’s displacement from its starting position is [imath]s = -117[/imath] meters.

I will say the given equation works if the ball is thrown downward, making alll vector quantities point in the same direction. The negative values of [imath]s, \, u_0, \, and \, g[/imath] can be treated as positive.

 

[JeffM]

This is a very poorly posed problem of projectile motion in the vertical direction.

First, the given equation should be [imath]s = u_0 t - \dfrac{1}{2}gt^2[/imath]
where [imath]s[/imath] is displacement (a vector quantity) of the ball from its initial position, not distance.
The value [imath]g =9.8 \, m/s^2[/imath] is the magnitude of the acceleration due to gravity near the Earth’s surface. A negative sign is necessary to indicate its direction since it is also a vector quantity.

Second, you are given the ball’s initial speed, not its velocity, Is the ball initially thrown upward or downward? That important piece of information is not stated.

Part (b) gives the position of the ball as 1/4 of the building’s height measured from the ground, or 39 meters.
That means the ball’s displacement from its starting position is [imath]s = -117[/imath] meters.

I will say the given equation works if the ball is thrown downward, making alll vector quantities point in the same direction. The negative values of [imath]s, \, u_0, \, and \, g[/imath] can be treated as positive.

I wish I could give a double or even triple “like“ to this post. I was thinking of giving a similar harsh assessment on the statement of the problem, but realized I could not do better than skeeter did.

I rather doubt that this problem has anything to do with a physics course that distinguishes between displacement and distance traveled or a calculus course that introduces vectors. The problem was posted under “arithmetic.” The problem can be fixed to make it into a decent one for a course in beginning algebra.

A ball is shot vertically downward at a velocity of 54 km per hour from the top of a building that is 156 meters tall. The distance traveled by the ball from the instant it is shot until it strikes the ground is given by the general formula of [imath]d = v_0t + \dfrac{gt^2}{2}[/imath], where t is time in seconds since the ball was shot, [imath]v_0[/imath] is the initial velocity in meters per second, and g = 9.8. (The g represents the effect of gravity close to the earth’s surface.)

(a) In this specific case, what is the numeric value that should be given to [imath]v_0[/imath]?

(b) How long will it take before the ball reaches a point that is one quarter of the way up the building?

One does not need any knowledge of physics or calculus to do this problem, but the student was given this other piece of garbage. If the original poster is still reading, I understand why you are confused and will try to help with the reworded problem.

As Dr. Peterson said, can you confidently determine from the numbers given in the problem the answer to question a? If not, what gives you doubts?

EDIT: This is why it is so important for new posters to say what they are studying. We wasted a lot of intellectual firepower because we did not know what level of mathematical knowledge the poster has.

EDIT 2: The original poster did not assist the cause by blacking out the explanation given for the answers. That would have given some clue as to the level of sophistication involved and what might have been confusing to a beginning student in algebra.

 

[callummcgurr]

I wish I could give a double or even triple “like“ to this post. I was thinking of giving a similar harsh assessment of the statement of the problem, but realized I could not do better than skeeter did.

I rather doubt that this problem has anything to do with a physics course that distinguishes between displacement and distance traveled or a calculus course that introduces vectors. The problem was posted under “arithmetic.” The problem can be fixed to make it into a decent one for a course in beginning algebra.

A ball is shot vertically downward at a velocity of 54 km per hour from the top of a building that is 156 meters tall. The distance traveled by the ball from the instant it is shot until it strikes the ground is given by the general formula of [imath]d = v_0t + \dfrac{gt^2}{2}[/imath], where t is time in seconds since the ball was shot, [imath]v_0[/imath] is the initial velocity in meters per second, and g = 9.8.

(a) In this specific case, what is the numeric value that should be given to [imath]v_0[/imath]?

(b) How long will it take before the ball reaches a point that is one quarter of the way up the building?

One does not need any knowledge of physics or calculus to do this problem, but the student was given this piece of garbage. If the original poster is still reading, I understand why you are confused and will try to help with the reworded problem.

As Dr. Peterson said, can you confidently determine from the numbers given in the problem the answer to question a? If not, what gives you doubts?

Hello thanks for your response. Your correct this is not from a physics course its part of a mathematics module i am currently doing. I think ive managed to get my head round this after doing more practise questions.

 

[skeeter]

Agree ... hence the reason I made that final statement about the original equation's validity if all vector quantities are in the same direction. The possibility that the initial velocity was upward in direction, opposite to acceleration & displacement, prompted me to write my previous post.

 

[JeffM]

Agree ... hence the reason I made that final statement about the original equation's validity if all vector quantities are in the same direction. The possibility that the initial velocity was upward in direction, opposite to acceleration & displacement, prompted me to write my previous post.

Oh I noticed your final sentence. Between you and Dr. Peterson, you had detangled the mess. Poor student.

 

[JeffM]

Hello thanks for your response. Your correct this is not from a physics course its part of a mathematics module i am currently doing. I think ive managed to get my head round this after doing more practise questions.

Good! Glad you got it.

Just remember: the more information you give, the better we can help.

By the way, when I said "poor student," I did not mean "bad student." I meant "unfortunate student." Badly worded problems are not usually a problem for those who have been using mathematics for many years, but they are almost always a nightmare for beginning students.