Homework Help: Kinematics problem, is it possible to solve with given information?

pyx · Sep 23, 2012

1. The problem statement, all variables and given/known data
A missile is launched from a silo 50m deep. After 20 seconds the engine stops, there is a 10 second period where the rocket is coasting straight up. At the end of this period, the rocket is 8000m above the ground.

a) What is initial acceleration of rocket?

b) What is rocket's velocity as it passes 8000m?

v0=0m/s
v1=?
v2=?
t0=0s
t1=20s
t2=t1+10s=30s
a0=?
a1=-9.8m/s^2
y0=-50m
y1=?
y2=8000m

2. Relevant equations
Kinematics equations

3. The attempt at a solution

Tried solving for the y1 value, but need v1, can't find v1 without a0, can't find a0 without y1 or v1. I am very lost. I feel like there isn't enough information to solve, but there is probably some trick to this and I am missing it. Help please! Thanks

NasuSama · Sep 23, 2012

pyx said: ↑

1. The problem statement, all variables and given/known data
A missile is launched from a silo 50m deep. After 20 seconds the engine stops, there is a 10 second period where the rocket is coasting straight up. At the end of this period, the rocket is 8000m above the ground.

a) What is initial acceleration of rocket?

b) What is rocket's velocity as it passes 8000m?

v0=0m/s
v1=?
v2=?
t0=0s
t1=20s
t2=t1+10s=30s
a0=?
a1=-9.8m/s^2
y0=-50m
y1=?
y2=8000m

2. Relevant equations
Kinematics equations

3. The attempt at a solution

Tried solving for the y1 value, but need v1, can't find v1 without a0, can't find a0 without y1 or v1. I am very lost. I feel like there isn't enough information to solve, but there is probably some trick to this and I am missing it. Help please! Thanks

Well, the first part of the question asks you to find the acceleration before the rocket has the constant acceleration, therefore having the constant velocity. To answer the question for the first part, we need to break into parts.. We know that:

→v_0 = 0 m/s
→t = 20 s
→d = 50 m

Then, this is enough to answer the question. You need to use this formula:

d = v_0 * t + ½ * a * t²

Given the values, solve for a.

pyx · Sep 23, 2012

So

50m=0m/s(20s)+.5(a)(400s^2)
50m=0m+200s^2(a)
0.25m/s^2=a
so a = 0.25m/s^2?

That is a pretty slowly accelerating rocket...

I didn't think that d=50m. The rocket starts 50 meters underground, I don't know the height after 20 seconds. How can d=50m?

NasuSama · Sep 23, 2012

pyx said: ↑

So

50m=0m/s(20s)+.5(a)(400s^2)
50m=0m+200s^2(a)
0.25m/s^2=a
so a = 0.25m/s^2?

That is a pretty slowly accelerating rocket...

I didn't think that d=50m. The rocket starts 50 meters underground, I don't know the height after 20 seconds. How can d=50m?

Oops. My bad. Then, we have...

s = 50 + v_0t + ½at²

Good thing you catch that mistakes! Without you, I would not notice the mistakes I make!

pyx · Sep 23, 2012

OK, with that I don't know s or a...so how do I solve that?

NasuSama · Sep 23, 2012

pyx said: ↑

OK, with that I don't know s or a...so how do I solve that?

s is the displacement
a is acceleration

pyx · Sep 23, 2012

I am still completely lost. I need to know the height after 20 seconds, as well as the velocity at 20 seconds and 30 seconds and the acceleration of the first part. No idea. Every equation I use has 2 unknowns.

NasuSama · Sep 23, 2012

pyx said: ↑

I am still completely lost. I need to know the height after 20 seconds, as well as the velocity at 20 seconds and 30 seconds and the acceleration of the first part. No idea. Every equation I use has 2 unknowns.

Oops. Sorry about that.

Hm... Before 20 seconds, we know that:

→the rocket is 50 m above the ground.
→v_0 = 0
→v_f = ?
→a > 0
→t = 20

So you use this form d_1 = h_0 + v_0 * t + ½ * a * t² = ½ * a * t². Clearly, d_1 =50 + ½ * a * t².

Between 20 and 30 seconds, since the rocket coasts up, we can say that a = 0, and that v_0_n = some velocity. Also, we need to determine the time interval between 30 seconds and 20 seconds; otherwise, if you just let t = 30, then you are answering the question wrong. It's after 20 seconds, we have the rocket having the zero acceleration and constant velocity (so that is the 10 second difference.). We should get:

d_2 = v_0_2 * Δt [where Δt is the difference between the time periods.]

Add up the distance and set that equal to 8000. We obtain:

d_1 + d_2 = 8000
50 + ½ * a * 20² + v_0_n * 10 = 8000
½ * a * 20² + v_0_n * 10 = 7950

Actually, you are correct. This problem seems to be impossible to solve!

pyx · Sep 23, 2012

The rocket starts at 50 meters BELOW ground. Not above.

NasuSama · Sep 23, 2012

pyx said: ↑

The rocket starts at 50 meters BELOW ground. Not above.

Then, it's just this:

½ * a * 20² + v_0_n * 10 = 8000

All we have is just a/30 = (sum of all accelerations = a + 0)/(10 + 20).

At the first 20 seconds, a > 0. Then, after 20 seconds, a = 0.

pyx · Sep 23, 2012

There has got to be a way to solve this. What about substitutions? Would that help any?

NasuSama · Sep 23, 2012

pyx said: ↑

There has got to be a way to solve this. What about substitutions? Would that help any?

Oh! I forgot to mention. Between t = 20 and t = 30, we have the same velocity as usual (rocket coasting up). This goes the same after the acceleration at t = 20. Use the acceleration formula: a = v_f/t, so we have...

½ * v_f/20 * 20² + v_f * 10 = 8000

Solve for v_f and find a using a = v_f/(overall time elapsed) = v_f / 30.