AP Physics - Freely Falling Objects

[Blodwynne]

I. A model rocket is launched straight upwards with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s2 until it's engines stop at an altitude of 150 m.

I found a thread with an extremely similar question, but the only reply that showed up was a formula, which didn't list the meanings of the variables. I'm pretty sure I could solve this if someone could help me to fill out a data table like this:

Initial Velocity: 50.0 m/s
Final Velocity: 0.0 m/s ?
Change in Velocity:
Average Velocity:
Acceleration:
Distance: x
Time:

I only need enough variables to solve, and even then just a springboard to give me the right direction. I'm getting confused by the rocket accelerating to a certain point and then coasting past.

II. Two students are on a balcony 19.6 m above the street. One student throws aball vertically downward at 14.7 m/s; at the same instant, the pther student throws a ball vertically upward at the same speed. What is the difference of the two balls' time in the ai, and what is the velocity of each ball as it hits the ground?

Part of what is confusing me here is the vertically downward phrase, and how that effects the acceleratin (assuming -9.8 m/s2 is used here)

Data Table

Initial Velocity: -14.7 m/s (B1), 14.7 m/s (B2)
Final Velocity:
Change in Velocity:
Average velocity:
Acceleration: -9.8 m/s2
Distance: 19.6 m
Time

Again, just need to know enough variables to use an equation and/or a step in the right direction.

Thanks!

 

[hage567]

Question 1:
So what exactly are you trying to find? Maximum altitude? The way to approach this is to break it up in sections. One when it's accelerating, one when it's not. You can use information from one section to find stuff that will be useful in the other section.

Question 2:
Have you drawn this out and labeled it? Based on what is given, what do you think you can work out? You will need to use more than one equation to get your final answer.

Take a look at your kinematics equations for projectile motion.

 

[baba89]

For the first question, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We know that the final velocity is 0 m/s, and the initial velocity is 50.0 m/s. We also know that the acceleration is 2.00 m/s2. Using this information, we can solve for the time it takes for the rocket to reach an altitude of 150 m.

v = u + at
0 = 50.0 + 2.00t
-50.0 = 2.00t
t = -50.0/2.00
t = 25 seconds

So, it takes 25 seconds for the rocket to reach an altitude of 150 m.

As for the second question, we can use the same equation v = u + at, but we have to consider the direction of the velocity. Since one ball is thrown vertically downward, its initial velocity is -14.7 m/s, while the other ball thrown vertically upward has an initial velocity of 14.7 m/s.

For the first ball, using v = u + at, we get:

v = -14.7 - 9.8t

For the second ball, using v = u + at, we get:

v = 14.7 - 9.8t

We know that the final velocity for both balls will be 0 m/s when they hit the ground. So, we can set these equations equal to 0 and solve for t.

For the first ball:

0 = -14.7 - 9.8t
14.7 = 9.8t
t = 14.7/9.8
t = 1.5 seconds

For the second ball:

0 = 14.7 - 9.8t
14.7 = 9.8t
t = 14.7/9.8
t = 1.5 seconds

So, both balls take 1.5 seconds to reach the ground. The difference in their time in the air is 0 seconds.

To find the velocity of each ball as it hits the ground, we can use the equation v = u + at again. Plugging in the values for t and a, we get:

For the first ball:
v = -14.