# Mechanics problems involving velocity,acceleration and gravity

1. Feb 27, 2012

### Conor11

1. The problem statement, all variables and given/known data
Hello, i have an exam in two days and spent all day trying to solve mechanic questions. Theres 4 in total, i'm having extreme trouble do not have the sufficient time to spend as i have other topics to cover. Would you please be able to help me out. Thanks the questions are as follows.

1: The rear of a bicycle passes a point O on a road waith a velocity of 4 m/s and an acceleration of 2m/s2. Four seconds later the front of a car paases 0 with a velocity of 2m/s and an acceleration of 4m/s2. When and how far from O does the front of the car meet the rear of the bicycle?

2.A stone is dropped from the top of a cliff which is 100m high. At the same time another stone is vertically thrown upwards from the foot of the cliff woth a speed of 40m/s.AT what height and when do the stones meet?

3.A Balloon starts from rest on the ground and rises vertically with a constant acceleration of 2m/s2. After 8 seconds a stone is dropped from the bottom of the balloon. How long does it take the stone to reach the ground.

4. A stone is thrown verticaly upwards from a point with an initial speed of 50m/s. Three seconds later another stone is thrown vertically up from the same pont witha speed of 70m/s. How long after the first stone leaves the ground do the two stones meet? At what height above the ground do the 2 stones meet?

2. Relevant equations

Linear motion with constant acceleration equations

1. v= u + at
2 s=ut +1/2at(squared)
3. v(squared)=u(squared)+2as

3. The attempt at a solution
1. s1. ut +1/2at(squared)
=4t +1/2(2)t(squared)
=4t + t(squared)

2. Feb 27, 2012

### LawrenceC

"1: The rear of a bicycle passes a point O on a road waith a velocity of 4 m/s and an acceleration of 2m/s2. Four seconds later the front of a car paases 0 with a velocity of 2m/s and an acceleration of 4m/s2. When and how far from O does the front of the car meet the rear of the bicycle?"

You have the formula for the distance given an initial velocity and acceleration rate. When they collide, what can you say about the distances travelled by each?

3. Feb 27, 2012

### Conor11

they have travelled the same length from O?

4. Feb 27, 2012

### tiny-tim

Welcome to PF!

Hi Conor11! Welcome to PF!

(try using the X2 button just above the Reply box )
yup, the bike moves with s = 4t + t2,

and obviously you've also worked out that the car moves with s = 2t + 2t2

but they're not the same t !

so you need to give them different names (eg t1 and t2), and find a third equation relating t1 to t2

what would that be?

(a lot of these exam problems involve giving things names! )

5. Feb 27, 2012

### LawrenceC

Yes, that is correct. But the times differ by 4 seconds so when you equate the distances, one of the times is (t-4). Solve for t, discard the time that makes no sense and use the other to determine the distance. Both equations will give same distance but one is evaluated at (t-4).

6. Feb 28, 2012

### Conor11

Oh i see , you get two equations, let them equal and then choose the one that makes sense. And then sub it back into the original to get the distance. Cheers Tim and Lawrence. Can you help me with the others?

Last edited by a moderator: Mar 28, 2012
7. Feb 28, 2012

### tiny-tim

show us what you've tried, and where you're stuck, and then we'll know how to help!

8. Feb 28, 2012

### Conor11

ok fair enough well:

do you sub in 100,9.8,and 0 in s=ut +1/2at^2 and then you get 100= 4.9t^"

Then, the same with the other stone or what equation do you use?

9. Feb 28, 2012

### Conor11

*t^2

10. Feb 28, 2012

### tiny-tim

yes, one equation each stone, using different names for s,

and a third equation relating those two s's …

show us what you get

11. Mar 28, 2012

### Conor11

Help with frequency and wave question please.?
Vibrations from a 400hz tuning fork set up a stationaery waves on a string whihc is fixed at both ends. The speed of the waves on the string is 500m/s. The stationery wave has only 5 antinodes along it. What is the length of the string?

12. Mar 28, 2012

### Conor11

Sorry how do you make a new post on PF?

13. Mar 28, 2012

### Staff: Mentor

Use the "New Topic" button in the upper left of the main Intro Physics forum window.