Projectile Motion: Ball A vs. Ball B - Which Reaches Ground First?

In summary, the ball will travel the same distance but will reach the ground faster due to the extra force applied in the horizontal direction.
  • #1
physio
68
1
A ball A is released from rest at a height of h and another ball B is provided with a horizontal force at the same height h. Both the balls fall to the ground. Which ball will reach the ground first?

Doesn't ball A reach the ground first because the ball B is applied with a horizontal force and so will remain in air for a longer time...?

Do they both fall to the ground at the same time??
 
Physics news on Phys.org
  • #2
They both fall to the ground at the same time. A force applied in the horizontal direction doesn't affect its motion in the vertical direction.
 
  • #3
yes but how and why... doesn't it defy conventional wisdom that it will be away from the ground for a longer time?
 
  • #4
physio said:
yes but how and why... doesn't it defy conventional wisdom that it will be away from the ground for a longer time?

Because the ball that goes away has initial "away" speed. Time for both are equal but the one with "away" property will perform better. It has added capability to go down and away.
 
  • #5
What do you mean by:-

Time for both are equal but the one with "away" property will perform better. It has added capability to go down and away.

I don't understand...
 
  • #6
I guess your understanding is that the body has to go down to the ground AND then move forward. So your reasoning that it need more time for 2 motions.

The body can do 2 jobs at a time.
In 1 sec, it can go down and that within that interval also it goes forward.
So if you find a value that it goes down, that interval also it does another job, moving forward.

I call it Multitasking.
 
  • #7
k thanks..got what you meant! :)
 
  • #8
If you really wanted to you could write equations for the distance the two balls travel through the air and their velocity. The one given a horizontal push obviously travels further through the air (in a curved path) but it also moves faster through the air due to the extra force acting on it. If you then worked out Time = distance/velocity you would find the extra velocity and extra distance "cancel" so the total time of flight is the same and both balls hit the ground together (ignoring air resistance).

However the maths is a lot easier if you realize that you can work out the vertical and horizontal components separately! This trick can even be used where the horizontal push isn't exactly horizontal. In that case you would work out what the vertical and horizontal components of the push were and then solve the equations for vertical and horizontal motion separately. Obviously in this case the balls would not reach the ground at the same time.

The classic school homework question involves a cannon pointed up at some angle and asks you to work out how far the ball will go. Again the way to approach it it to write separate equations for the vertical and horizontal motion. Remembering that as the ball reaches peak altitude the vertical component of it's velocity is zero and that the flight time both vertically and horizontally is the same.
 
Last edited:

1. What is projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. It is a type of motion that follows a curved path, known as a parabola.

2. How is the initial velocity of a ball thrown calculated in projectile motion?

The initial velocity of a ball thrown in projectile motion can be calculated using the equation v0 = vf - at, where v0 is the initial velocity, vf is the final velocity, a is the acceleration due to gravity (9.8 m/s2), and t is the time elapsed.

3. What is the maximum height reached by a ball thrown in projectile motion?

The maximum height reached by a ball thrown in projectile motion can be calculated using the equation h = (v02sin2θ)/2g, where h is the maximum height, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity (9.8 m/s2).

4. How does air resistance affect the trajectory of a ball thrown in projectile motion?

Air resistance can affect the trajectory of a ball thrown in projectile motion by slowing down its speed and altering its path. As the ball moves through the air, it experiences a force of drag that opposes its motion, causing it to deviate from its ideal parabolic path.

5. What are some real-life applications of projectile motion?

Projectile motion has various real-life applications, including sports such as basketball, baseball, and football, where players need to accurately throw or kick a ball to reach a target. It is also used in military applications for predicting the trajectory of missiles and artillery shells. Additionally, it is used in physics experiments to study the effects of gravity and air resistance on objects in motion.

Similar threads

Replies
17
Views
17K
Replies
2
Views
667
  • Introductory Physics Homework Help
Replies
5
Views
206
Replies
3
Views
1K
  • Classical Physics
2
Replies
64
Views
2K
Replies
5
Views
1K
Replies
6
Views
680
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
34
Views
555
  • Introductory Physics Homework Help
2
Replies
38
Views
1K
Back
Top