Ball and Runner: Catching at the Bottom of a Building

In summary, a ball is thrown from a 25m tall building with an initial speed of 12m/s. At the same time, a person is running at a distance of 31m from the building. To catch the ball at the bottom of the building, the person's average speed must be determined. The equations used to find the final velocity and time of the ball's descent were V^2=Vinti^2+ax and Vfinal= Vinitial+at. The equation y=Vinitialt+0.5at^2 was used to find the time for the ball to hit the ground.
  • #1
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Homework Statement



A ball is thrown from top of a 25m tall building. The balls initail speed is 12m/s. At the same instant a person is running on the ground at the distance of 31m from the building. What must be the avg speed of the person if he is to catch the ball at the bottem of the building?

Homework Equations


Ball
V initial = +12m/s
x= 25m
t=?
a= -9.8m/s^2

so i use the equation V^2=Vinti^2+ax to find the final v
and then use the Vfinal= v initial+at to find the time the ball hits the ground
and use this time to find the avg velocity of the boy running to the building

The Attempt at a Solution


Am i taking the right steps thank you
 
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  • #2
Do you need the final velocity?
You know Vinit and distance - you want time
What's the motion equation for distance/time/Vinit ?

ps V^2=Vinti^2+2ax by the way.
 
  • #3
mgb_phys said:
Do you need the final velocity?
You know Vinit and distance - you want time
What's the motion equation for distance/time/Vinit ?

ps V^2=Vinti^2+2ax by the way.

do i use the equa y=vinitial t +.5 at^2
 
  • #4
Yes, watch the signs of v and a
 

1. What is a freely falling body?

A freely falling body is an object that is falling under the influence of gravity with no other forces acting upon it. This means that the only force acting on the body is the force of gravity.

2. What factors affect the rate of free fall?

The rate of free fall is affected by the mass of the object and the acceleration due to gravity. The more massive the object, the faster it will fall. The acceleration due to gravity is a constant value of 9.8 meters per second squared on Earth.

3. What is the difference between free fall and terminal velocity?

Free fall is the initial stage of falling where the object is accelerating due to gravity. Terminal velocity is the maximum velocity that a falling object can reach when the upward force of air resistance is equal to the downward force of gravity. At this point, the object will no longer accelerate and will fall at a constant speed.

4. How does air resistance affect freely falling bodies?

Air resistance is a force that opposes the motion of a falling object, causing it to slow down. As an object falls, it accelerates due to gravity, but as it gains speed, the force of air resistance also increases, eventually balancing out the force of gravity and causing the object to reach terminal velocity.

5. Does the mass of an object affect its rate of fall?

Yes, the mass of an object does affect its rate of fall. According to Newton's Second Law of Motion, the force exerted on an object is equal to its mass multiplied by its acceleration. This means that a more massive object will experience a greater force of gravity and will therefore accelerate faster than a less massive object.

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