Projectile Motion Problems: Solving for Time with Given Initial Speed and Height

[Sophialiu609]

t=number of seconds
h=height
r=initial speed
How do you solve these two problems?
1. A projectile is fired upward with an initial speed of 2940 m/s. After how many minutes does it hit the ground?
2. A ball is thrown upward from the top of a 98m tower with an initial speed of 39.2 m/s. When does it hit the ground?
I don't understand how you can find the answers to these types of problems

 

[Sophialiu609]

Help PLEASE!
I got this far on the second one...
h=rt- 4.9t²
-98=39.2t-4.9t²
-20=8t-t²
0=-(t²-8t -20)
0=-(t-10)(t+2)
(t-10)=0 (t+2)=0
t=10 t=-2

 

[apoptosa]

For the first:
If you don't need the height then why are you calculating it ?
Try Vf = Vi + at
Where t would be time of flight & Vf,Vi final and initial velocity respectively

 

[Sophialiu609]

Well, I'm supposed to put the problem into that formula, that's what I'm confused about.

 

[rocomath]

Don't forget to convert time to minutes b/c the answer you will get is in seconds.

 

[t!m]

For the first, if it's fired from the ground and lands on the ground, what is h (often times, more appropriately written as \Deltah)?

 

[hage567]

Well, I'm supposed to put the problem into that formula, that's what I'm confused about.

For the first question: you can use the same equation as you did for problem #2. If the projectile returns to the ground, what is its displacement? What does that make h in your equation?

 

[Sophialiu609]

Ok, so what I have so far is
0=2940t/60 -4.9t^2/60
0=-4.9t(t/60 -1)
0=-4.9t(t-1/60)
0=-4.9t(t-1)
t={0,1}
Is that right?

 

[Sophialiu609]

0=2940t-4.9t²
60 60
0=2940t-4.9t²
0=600t-t²
0=-t(t-600)
-t=0 (t-600)=0
t=0 t=600

or is this right?

 

[apoptosa]

Just a little tip, you might want to work through things in algebra before you number plug :)

 

[rocomath]

Would time 0 make sense as an answer?

And what units are your answers in?

 

[Sophialiu609]

0 wouldn't make sense as an answer, my answer is in minutes~I think... but now I'm more confused...

 

[Sophialiu609]

Is it 10 minutes...?

 

[rocomath]

Is it 10 minutes...?

Stop guessing. What equation are you using?

And before plugging values into your equation, let's SOLVE for the variable we want.

 

[Sophialiu609]

The one I posted as the title!
h=rt-4.9t^2

 

[rocomath]

The one I posted as the title!
h=rt-4.9t^2

Well looks right to me. You have it in terms of minutes, so there you go.

 

[Sophialiu609]

So was my answer correct? 10 minutes? Because 600/60=10

 

[Sophialiu609]

oh ohkay, thank you i didn't see the second page