Velocity, time, acceleration etc

• lauriecherie
In summary, the conversation discusses a problem involving a hot air balloon ascending at a rate of 13 m/s and a package being dropped over the side. The question asks for the time it takes for the package to reach the ground and the speed at which it hits the ground. The equations provided are used to solve the problem, but the individual is having trouble with motion in two directions. However, it is clarified that the motion is only in one dimension and the quadratic formula can be used to solve for time in the equation x = Xo + Vo*t - 1/2*g*t2.
lauriecherie

Homework Statement

A hot air balloon is ascending at the rate of 13 m/s and is 93 m above the ground when a package is dropped over the side. How long does the package take to reach the ground? With what speed does it hit the ground?

Homework Equations

x(t)= initial position + final velocity * time

v(t)= (acceleration * time) + initial velocity

x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time) + inital position

x= initial position * (average velocity * time)

average velocity= (final velocity - initial velocity) / (2)

(final velocity^2) - (initial velocity^2) = 2 * acceleration * change in position

The Attempt at a Solution

I manipulated equation 4 to solve for time and got 7.15 s, which is wrong. Then I began thinking "Do I need to double this time?" Is it supposed to be 14.31 s?
For question 2, I used the last equation to solve for final velocity and got 50.86 m/s which it also marked incorrectly. Can anyone please explain this to me? I seem to be having trouble with motion in two direction thing...

It's only motion in one dimension. You just need to set up your equation.

Use:

x = Xo + Vo*t - 1/2*g*t2

Xo is your initial height. Vo is your velocity (+ is up)

The third term is -, as g is down.

LowlyPion said:
It's only motion in one dimension. You just need to set up your equation.

Use:

x = Xo + Vo*t - 1/2*g*t2

Xo is your initial height. Vo is your velocity (+ is up)

The third term is -, as g is down.

I'm solving for time. I don't know how to manipulate that equation to get time by itself. Is there another one on here I can use?

1. What is velocity?

Velocity is a measure of the rate at which an object's position changes with respect to time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position (displacement) by the change in time. It can also be calculated by multiplying an object's speed by its direction.

3. What is the difference between speed and velocity?

Speed is a scalar quantity, meaning it only has magnitude, while velocity is a vector quantity that also takes direction into account. In other words, speed tells us how fast an object is moving, while velocity tells us how fast and in which direction it is moving.

4. What is the difference between velocity and acceleration?

Velocity is a measure of an object's change in position over time, while acceleration is a measure of an object's change in velocity over time. In other words, acceleration tells us how quickly an object's velocity is changing, while velocity tells us the object's speed and direction.

5. How does time affect velocity and acceleration?

In general, velocity and acceleration are both dependent on time. The longer an object is accelerating, the greater its change in velocity will be. Similarly, the longer an object is moving with a certain velocity, the greater its change in position will be.

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