Solve Kinematics Problem: Initial Velocity of Ball Thrown Horizontally

In summary, the ball is thrown horizontally from a 35 m high building and strikes the ground 80 m from the base of the building. To find the initial velocity, the time it takes for the ball to reach the ground is first calculated using the x=V0t + 1/2 at^2 formula. Then, this time is used to solve for acceleration using the Vf^2 = V0^2 + 2ax formula. Finally, the initial velocity is found by plugging in the acceleration and time into the x = V0t + (1/2) a t ^2 formula. However, there may have been some confusion with concepts as the correct answer given in the book is 30 m
  • #1
PinkFlamingo
19
0
A ball is throw horizontally from the top of a building 35 m high. The ball strikes the ground at a point 80 m from the base of the building. Find the ball's initial velocity.

What I have done so far is to find the time it takes for the ball to reach the ground, using the x=V0t + 1/2 at^2 forumula, and I found the time to be 2.67 s.

Then I used that and plugged it into the Vf^2 = V0^2 + 2ax formula, and solved for a, finding it to be [-V0^2]/160

and then I plugged that into the x = V0t + (1/2) a t ^2 formula, and solved the quadratic equation, and found the initial velocity to be 60 m/s, but in my book it says that the answer is 30 m/s I just can't gigure out what I did wrong.
 
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  • #2
Here, you have mixed up your concepts a bit.

The ball experiences FREE FALL!
Therefore, you know at the start its acceleration; in vectorial form it is [tex]\vec{a}=-g\vec{j}[/tex]
There is no acceleration in the horizontal direction; try and use the free fall condition to solve the problem properly.
 
  • #3
Try starting in the y-direction. As arildno said, you know the distance the ball travels, the velocity it starts with (in that direction) and the acceleration is g. See what you can find out about that and than start looking at the x-direction motion.
 

1. What is kinematics?

Kinematics is the study of motion, including the position, velocity, and acceleration of objects.

2. How do you solve a kinematics problem for the initial velocity of a ball thrown horizontally?

To solve for the initial velocity of a ball thrown horizontally, you can use the equation v = d/t, where v is the velocity, d is the distance traveled, and t is the time it took to travel that distance. You can also use the equations of motion, such as v = u + at, where u is the initial velocity, a is the acceleration (which is 0 for a horizontally thrown ball), and t is the time.

3. What information do I need to solve a kinematics problem for the initial velocity of a ball thrown horizontally?

To solve for the initial velocity of a ball thrown horizontally, you will need to know the distance the ball traveled and the time it took to travel that distance. You may also need to know the acceleration, if it is not 0.

4. What are some common mistakes when solving kinematics problems for the initial velocity of a ball thrown horizontally?

Some common mistakes when solving kinematics problems for the initial velocity of a ball thrown horizontally include not using the correct equations, not converting units correctly, and not considering the direction of motion (which is horizontal in this case).

5. How can I check if my solution for the initial velocity of a ball thrown horizontally is correct?

You can check your solution by plugging the values you calculated into the original equations and making sure they satisfy the given information. You can also use common sense and consider if your solution makes sense in the context of the problem. Additionally, you can use online calculators or ask a peer or instructor to check your work.

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