Linear and projectile motion?

In summary, the question asks for the initial velocity of a ball that is thrown downward from a 65.0 m tall tower and takes 1.30 seconds to hit the ground. Using the formula x = vi.t + 0.5.a.t^2, the initial velocity can be calculated to be 43.6 m/s. The original attempt at using the formula Vi = Vf - aT was incorrect as the final velocity was not given.
  • #1

Homework Statement


A ball is thrown downward from a tower 65.0 m tall. If the ball takes 1.30 seconds to hit the ground, what was its initial velocity?

The answer my teacher provides is 43.6 m/s, but I am having a problem reaching that answer.

Homework Equations


Possibly Vi = Vf - aT? This is the equation I am trying to use, but the final velocity is not given, I don't think.


The Attempt at a Solution


First, I tried Vi = 0 + 9.8 x 1.3, but obviously, it doesn't work. So whether there is information missing or I am using the wrong formula, I don't know. Any help would be appreciated!
 
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  • #2
killjoy2019 said:

Homework Statement


A ball is thrown downward from a tower 65.0 m tall. If the ball takes 1.30 seconds to hit the ground, what was its initial velocity?

The answer my teacher provides is 43.6 m/s, but I am having a problem reaching that answer.

Homework Equations


Possibly Vi = Vf - aT? This is the equation I am trying to use, but the final velocity is not given, I don't think.


The Attempt at a Solution


First, I tried Vi = 0 + 9.8 x 1.3, but obviously, it doesn't work. So whether there is information missing or I am using the wrong formula, I don't know. Any help would be appreciated!

The values you have are:

x - displacement - 65
a - acceleration due to gravity - 9.8
t - time - 1.3

All motion and acceleration is down, so I have made all values positive

You want vi

so you need the motion formula with out the final velocity. That is

x = vi.t + 0.5.a.t2

sub values into that and see how you go.
 
  • #3
Thank you! That seem to have worked. (: I knew there was something wrong with the formula I was using.
 
  • #4
killjoy2019 said:
Thank you! That seem to have worked. (: I knew there was something wrong with the formula I was using.

You should always identify those values you know, and the value(s) you want, to help in deciding which formula to use.
 
  • #5


I would like to clarify that there are two types of motion being discussed here - linear motion and projectile motion. Linear motion refers to the motion of an object in a straight line, while projectile motion refers to the motion of an object that is projected into the air and follows a curved path due to the influence of gravity.

In this problem, we are dealing with projectile motion as the ball is thrown downward from a tower. To solve for the initial velocity, we can use the equation Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2), and t is the time (1.30 seconds).

Since the ball is thrown downward, the initial velocity will be negative. Therefore, we can rewrite the equation as -Vf = Vi - at. Plugging in the given values, we get:

-Vf = Vi - (9.8 m/s^2)(1.30 s)
-Vf = Vi - 12.74 m/s

We also know that the final velocity when the ball hits the ground will be 0 m/s. Therefore, we can rewrite the equation as 0 = Vi - 12.74 m/s and solve for Vi:

Vi = 12.74 m/s

However, this is the magnitude of the initial velocity. Since the initial velocity is negative, we can write it as -12.74 m/s. But since the ball is thrown downward, the magnitude is more important in this case, so the answer would be 12.74 m/s.

It is possible that your teacher used a different approach or formula to solve for the initial velocity. But as long as you understand the concepts of projectile motion and how to use the appropriate equations, you should be able to arrive at the correct answer. I hope this helps!
 

1. What is the difference between linear and projectile motion?

Linear motion is when an object moves along a straight path, while projectile motion is when an object is launched into the air and follows a curved path due to the influence of gravity.

2. What are some examples of linear motion?

Some examples of linear motion include a car moving along a straight road, a person walking in a straight line, or a train traveling on a straight track.

3. How is projectile motion affected by gravity?

Gravity affects projectile motion by pulling the object towards the center of the Earth, causing it to follow a curved path. As the object moves higher, the force of gravity decreases, and the object will eventually fall back to the ground.

4. What are the factors that influence the trajectory of a projectile?

The factors that influence the trajectory of a projectile include its initial velocity, angle of launch, air resistance, and the force of gravity.

5. How is linear and projectile motion used in real-world applications?

Linear and projectile motion are used in many real-world applications such as sports, transportation, and engineering. For example, understanding projectile motion is crucial for designing and launching rockets, and linear motion is used in the design of roller coasters and vehicles.

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