Using suvat to find time traveled by a cannonball

[Camden]

Homework Statement

In a Castle a cannon is in place to fire at ships.
One ship was hit by a cannonball at a horizontal distance of 150 metres from the cannon.
The height from the cannon above the castle was 67 metres
I need to show the time that was taken from the cannonball to hit the ship.
My attempt is in the attached photo
The answer is 3.7s but I’m not sure how to get to the answer.

Relevant Equations

Suvat equations
Trigonometry equations

Everything is in the photo

 

[jbriggs444]

Homework Statement:: In a Castle a cannon is in place to fire at ships.
One ship was hit by a cannonball at a horizontal distance of 150 metres from the cannon.
The height from the cannon above the castle was 67 metres
I need to show the time that was taken from the cannonball to hit the ship.
My attempt is in the attached photo
The answer is 3.7s but I’m not sure how to get to the answer.
Relevant Equations:: Suvat equations
Trigonometry equations

Everything is in the photo

You have a little section of the photo with:

Vertically
s = 67 m
u = 0 m/s
v =
a = 9.8 m/s²
t = 3.7 s

How did you obtain that t value?

 

[Camden]

You have a little section of the photo with:

How did you obtain that t value?

The t value was given to me
I had to prove that t was 3.7s

 

[jbriggs444]

The t value was given to me
I had to prove that t was 3.7s

That little section has the letters S U V A T in that order. Can you find a SUVAT equation that relates the values you know to the one you want to know? (The one you want to know is t).

 

[Camden]

That little section has the letters S U V A T in that order. Can you find a SUVAT equation that relates the values you know to the one you want to know? (The one you want to know is t).

Yes I am trying to find the t equation but I need to find distance over speed and I know the difference just what I’m stuck on is the speed

 

[jbriggs444]

Yes I am trying to find the t equation but I need to find distance over speed and I know the difference just what I’m stuck on is the speed

You have initial velocity, acceleration and distance travelled. You want to determine time. Surely there is an equation relating those four quantities.

And no, you do not need to find distance divided by speed.

 

[Camden]

You have initial velocity, acceleration and distance travelled. You want to determine time. Surely there is an equation relating those four quantities.

Yes I need to find time but I also need to find final velocity. I don’t know which formula to use

 

[jbriggs444]

Yes I need to find time but I also need to find final velocity. I don’t know which formula to use

Well, I do not have a list of SUVAT formulas in a textbook because it has been some 40 years since I had a physics textbook. But Google is my friend. I bet I can find a complete list of SUVAT formulas pretty quickly.

Let's Google "suvat equations" and see what we get.

Wikipedia has an article -- "equations of motion". Wiki is pretty good, though with a tendency to get long winded and overly technical on occasion. We'd be better served by simplicity here. But let's give that article a try.

Here we go. They have a relevant section.

In elementary physics the same formulae are frequently written in different notation as:

$v=u + at$
$s = ut + \frac{1}{2}at^2$
$s = \frac{1}{2}(u + v)t$
$v^2 = u^2 + 2as$
$s = vt - \frac{1}{2}at^2$
[Re-rendered by hand -- I tried and failed to re-tag the LaTeX code in the original]

One of those equations relates the three quantities that you know with the one that you want to confirm.

[Five equations... Of course there are five. There are five variables - S, U, V, A and T. Each of the five equations leaves one of the variables out and relates the other four. I'd never bothered thinking about that until today. If you solved each equation in turn for each of its four variables, that would give you a list totaling twenty equations. I guess that would be useful for the algebra-challenged, but personally I hate memorization worse than algebra. As it turns out, a pre-cooked solution to a quadratic would be a lot messier than the special case we are faced with here, so algebra is our friend]

Once you get time, you can use it to determine final velocity.

 

[Camden]

Well, I do not have a list of SUVAT formulas in a textbook because it has been some 40 years since I had a physics textbook. But Google is my friend. I bet I can find a complete list of SUVAT formulas pretty quickly.

Let's Google "suvat equations" and see what we get.

Wikipedia has an article -- "equations of motion". Wiki is pretty good, though with a tendency to get long winded and overly technical on occasion. We'd be better served by simplicity here. But let's give that article a try.

Here we go. They have a relevant section.

One of those equations relates the three quantities that you know with the one that you want to confirm.

[Five equations... Of course there are five. There are five variables - S, U, V, A and T. Each of the five equations leaves one of the variables out and relates the other four. I'd never bothered thinking about that until today. If you solved each equation in turn for each of its four variables, that would give you a list totaling twenty equations. I guess that would be useful for the algebra-challenged, but personally I hate memorization worse than algebra. As it turns out, a pre-cooked solution to a quadratic would be a lot messier than the special case we are faced with here, so algebra is our friend]

Once you get time, you can use it to determine final velocity.

Thankyou!