Ball Release and Thrown to reach ground at the same time

In summary, to find the initial speed of the first ball thrown and the second ball dropped from a building of 20m height, we can use the equations Vf=Vo+a*t and X=Vo*t+1/2*a*t^2. By solving for the total time (3.02s), we can find the initial speed of the first ball to be g*t1, where t1 is the time it takes for the ball to reach its peak and return to its initial position. Using this equation, we can solve for Vo and find the correct solution.
  • #1
spikehoward

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 1.00s later. You may ignore air resistance. If the height of the building is 20m, what must the initial speed of the first ball be if both are to hit the ground at the same time?

Homework Equations


Vf=Vo+a*t
X=Vo*t+1/2*a*t^2

The Attempt at a Solution


Ball 1:
X=Vo*t+1/2*a*t^2
20=0+1/2*9.8*t^2
t=2.02s

Ball 2:
total time=1+2.02=3.02

The ball is thrown up, eventually comes to a rest, and then begins to fall so
Vf=0=Vo-g*t1 so Vo=g*t1

where t1 is the time it takes for the ball to reach its peak AND the time it will take to fall back to it original position. The velocity, Vo has the same magnitude and opposite direction and the point it is initially thrown and when it returns.

(1) Vo=g*t1
(2)20=Vo*t2+1/2*g*t2^2
(3) 2*t1+t2=3 where t2 is the time it takes to fall from the initial point to the bottom.

Can I use these three equation to solve? I get an answer that checks out but the solution manual says it is incorrect. Did I make a wrong assumption?
 
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  • #2
I think your equations should give the correct solution. I got a little confused at first because "Ball 1" in your solution is the "second ball" in the problem statement. But that's OK.

You are apparently taking downward as positive direction.

For the ball that is thrown upward, you don't have to break up the flight into parts. You can treat the entire flight in one equation. So, you don't need to deal with t1 and t2 at all. You just need the total time (3.02 s).
 

Related to Ball Release and Thrown to reach ground at the same time

1. What is the concept of "Ball Release and Thrown to reach ground at the same time"?

The concept of "Ball Release and Thrown to reach ground at the same time" is a basic principle of projectile motion. It states that when an object is released at an angle from a certain height, it will reach the ground at the same time as an object that is thrown horizontally from the same height, as long as air resistance is negligible.

2. How is this principle related to Newton's laws of motion?

This principle is related to Newton's laws of motion, specifically the first and second laws. The first law states that an object in motion will continue in motion in a straight line unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle of "Ball Release and Thrown to reach ground at the same time" follows these laws as the objects are in motion with constant acceleration due to gravity.

3. Does the mass of the object affect the outcome of this principle?

No, the mass of the object does not affect the outcome of this principle as long as air resistance is negligible. This is because the acceleration due to gravity is the same for all objects, regardless of their mass.

4. How does air resistance affect this principle?

Air resistance can affect this principle by slowing down the object in motion, causing it to take longer to reach the ground. This can cause the object released at an angle to reach the ground at a different time than the object thrown horizontally, as the angle of release can affect the amount of air resistance the object experiences.

5. What are some real-life examples of this principle?

Some real-life examples of this principle include throwing a ball off a cliff, firing a projectile from a cannon, and launching a rocket into space. In all of these examples, the object follows a curved path and reaches the ground at the same time as an object thrown horizontally from the same height.

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