Vertical Motion w/ constant acceleration

In summary, the problem involves a ball being thrown up from a building and another ball being dropped from the same building. The goal is to find the initial speed of the first ball so that both balls hit the ground at the same time. The equations that can be used to solve this problem are vf^2 = v0^2 + 2ax, vf = v0 + at, and x = x0 + v0t + 1/2at^2. The key is to focus on the last equation and set the "t" values as equal for both objects. This will allow us to solve for the initial speed of the first ball.
  • #1
cdlegendary
15
0

Homework Statement



A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.14 s later. You may ignore air resistance.

A.) If the height of the building is 20.6 m, what must the initial speed be of the first ball if both are to hit the ground at the same time?

Homework Equations



vf^2 = v0^2 + 2ax
vf = v0 + at
x = x0 + v0t + 1/2at^2

The Attempt at a Solution



I'm really not sure where to start. If someone could help me out I would greatly appreciate it.
 
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  • #2
Focus on the last of your three equations. "t" has to be the same for both objects: the one that's dropped, and the one that's thrown up.
 
  • #3
ideasrule said:
Focus on the last of your three equations. "t" has to be the same for both objects: the one that's dropped, and the one that's thrown up.

Hmm but wouldn't there be two unknowns for that equation? I tried setting the equation equal to itsel but it turned out kind of badly, haha...
 

1. What is vertical motion with constant acceleration?

Vertical motion with constant acceleration is the movement of an object in a vertical direction (up or down) with a constant rate of change in velocity. This means that the object is either increasing or decreasing its speed by the same amount for each unit of time.

2. How is vertical motion with constant acceleration different from free fall?

Vertical motion with constant acceleration is a specific type of motion where the object experiences a constant acceleration due to a constant force. Free fall, on the other hand, refers to the motion of an object falling under the influence of gravity alone, without any other forces acting upon it.

3. What is the formula for calculating vertical motion with constant acceleration?

The formula for calculating vertical motion with constant acceleration is:
s = ut + 1/2at^2
where s is the displacement (vertical distance traveled), u is the initial velocity, a is the acceleration, and t is the time elapsed.

4. How does air resistance affect vertical motion with constant acceleration?

Air resistance or drag can have a significant impact on vertical motion with constant acceleration, especially at high speeds. It acts in the opposite direction of the object's motion and can decrease the acceleration and velocity of the object.

5. Can vertical motion with constant acceleration be negative?

Yes, vertical motion with constant acceleration can be negative. This occurs when the acceleration and velocity of the object are in the opposite direction, such as when the object is traveling downward. In this case, the acceleration is considered to be negative and is denoted by a negative sign in the formula.

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