Calculating Free Fall Motion: A Practice Problem with Step-by-Step Solution

In summary, the problem involves a ball being shot horizontally off a cliff and landing a certain distance from the base. To find the time the ball was in the air, the equation x - Δx = vt - (1/2)at^2 can be used. To find the initial velocity, the second equation x - Δx = Vot + (1/2)at^2 can be used. However, since the ball is being shot horizontally with a certain velocity and dropped vertically, the equations should be adjusted accordingly. By setting the equation equal to 0 and using the given values for initial velocity and acceleration, the time can be found and used to calculate the initial velocity.
  • #1
tmc123
3
0

Homework Statement



The original question is:
A ball is shot horizontally off the edge of a cliff 35 m high. The ball lands 20 m from the base of the cliff.
a. How long was the ball in the air?
b. What was the initial velocity of the ball?

Homework Equations



I believe these would be helpful.
x - Δx = vt - (1/2)at^2
x - Δx = Vot + (1/2)at^2

The Attempt at a Solution



To find time, I have this:
20 = 0t - (1/2)(-9.8)t^2
20 = 4.9t^2
t = 2.02 sec

which I then plugged into the second equation to find Vo

20 = Vo (2.02) + (1/2)(-9.8)(2.02)^2
20 = 2.02 Vo - 20
40 = 2.02 Vo
Vo = 19.802 m/s

This unfortunately appears to be in error, but I am unsure where I went astray. I think it's something about the incorrect equations being used, or my not fully understanding the problem.
 
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  • #2
The ball is being shot horizontally with certain velocity, not given.
The ball is "dropped" vertically from rest and traveled distance given.
You can find time traveled by the ball to the base.
 
  • #3
Hi - just a quick question to clarify. When you say I can find the time by the ball to the base, are you saying that the x is irrelevant (so I should try setting my equation equal to 0 instead of 20?).
 
  • #4
x is the product of time and velocity. No forces acting horizontally, so acceleration is irrelevant.
y is given with initial velocity and acceleration(since there is force acting on it, gravity). From this you can find the time.
 
  • #5
Alright. I'll give that a try. Thank you.
 

1. What is free fall motion?

Free fall motion is the motion of an object under the influence of only gravity, with no other external forces acting on it. It is a type of motion where the only acceleration acting on the object is due to the force of gravity.

2. What is the acceleration of an object in free fall?

The acceleration of an object in free fall is approximately 9.8 meters per second squared (m/s²), which is the acceleration due to gravity on Earth. This means that the speed of the object increases by 9.8 m/s² every second it falls.

3. Why does an object in free fall not continue to accelerate indefinitely?

An object in free fall does not continue to accelerate indefinitely because of air resistance. As the object falls, it pushes against the air particles, causing them to resist the motion and create a force in the opposite direction. This force increases as the object's speed increases, eventually reaching a point where it balances out the force of gravity, resulting in a constant speed called terminal velocity.

4. How does the mass of an object affect its free fall motion?

The mass of an object does not affect its free fall motion. Two objects of different masses, dropped from the same height, will hit the ground at the same time because they experience the same acceleration due to gravity. However, a more massive object will have a greater weight, which means it will experience a stronger force of gravity and reach a higher terminal velocity.

5. Can an object experience free fall motion if it is not falling straight down?

Yes, an object can experience free fall motion even if it is not falling straight down. As long as the only force acting on the object is gravity and there is no resistance from the medium it is falling through, it will experience free fall motion. This can occur in situations such as a skydiver falling at an angle or a roller coaster dropping from a height.

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