[Kinematics] Don't know how to find value

Mar 2010
71
2
Crate is being lowered by a crane at a constant speed of 2 m/s when a ball falls out of the hole in the crate, it hits the floor 10s before the crate. Find the height of the crate when the ball fell out of the crate.

How do I find the height?

All formulas gave me 20 as the height.. which is wrong.
 

skeeter

MHF Helper
Jun 2008
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6,764
North Texas
Crate is being lowered by a crane at a constant speed of 2 m/s when a ball falls out of the hole in the crate, it hits the floor 10s before the crate. Find the height of the crate when the ball fell out of the crate.

How do I find the height?

All formulas gave me 20 as the height.. which is wrong.
let h = height of the crate when the ball drops out

ball's initial speed = 2 m/s

let t = time for the ball to hit the ground

t+10 = time for the crate to hit the ground

for the crate ...

\(\displaystyle
h = 2(t+10)
\)

for the ball (using 10 for g) ...

\(\displaystyle
h = 2t + 5t^2
\)

\(\displaystyle
2t + 5t^2 = 2(t+10)
\)

solve for t, then determine h
 
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Mar 2010
71
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Help please

Thanks skeeter. That helped, I got the right answer.

I got more questions I do not understand.

Edit: I forgot to specify what I'm actaully stuck on, the 5th question, where the skater is 2 seconds earlier than the cyclist. I'm just wondering how to put it on the graph. So, I assume SKATER:\(\displaystyle 160=12*22\), is that right?

A cyclist, passes the starting line \(\displaystyle t=0\)

The cyclist reaches the finish at \(\displaystyle (t=22)\)

What I have so far:
1- the distance of the starting from the finish line
\(\displaystyle 260m\)

2- the distance travelled after the finish line
\(\displaystyle 24m\)

3- the acceleration of the cyclist
\(\displaystyle -3ms^-2\)

4- the average speed of the cyclist from the starting to finish
\(\displaystyle 10ms^-1\)

5- A skater passed the starting line 2 seconds before cyclist. Skater is travelling at a constant speed of \(\displaystyle 11ms^-1\). Who wins the race and how much?
?
 
Last edited:

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Thanks skeeter. That helped, I got the right answer.

I got more questions I do not understand.

Edit: I forgot to specify what I'm actaully stuck on, the 5th question, where the skater is 2 seconds earlier than the cyclist. I'm just wondering how to put it on the graph. So, I assume SKATER:\(\displaystyle 160=12*22\), is that right?

A cyclist, passes the starting line \(\displaystyle t=0\)

The cyclist reaches the finish at \(\displaystyle (t=22)\)

What I have so far:
1- the distance of the starting from the finish line
\(\displaystyle 260m\) correct

2- the distance travelled after the finish line
\(\displaystyle 24m\) correct

3- the acceleration of the cyclist
\(\displaystyle -3ms^-2\) correct

4- the average speed of the cyclist from the starting to finish
\(\displaystyle 10ms^-1\) |v{avg}| = (260 m)/(22 s)

5- A skater passed the starting line 2 seconds before cyclist. Skater is travelling at a constant speed of \(\displaystyle 11ms^-1\). Who wins the race and how much? t = 260/11 = 23.6 s ... but he got a 2 second headstart, so the skater crosses the finish line at t = 21.6 s relative to when the cyclist started.
...

next time, start a new problem with a new thread.
 
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Mar 2010
71
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skeeter said:
...

next time, start a new problem with a new thread.
Understandable. Thanks for the help. (Solved)