Difficult Projectile Motion Problem

In summary, the player hit a ball at a 45º angle above the horizontal at a height of 1.3m. The ball cleared a 3m wall 130m away. The initial velocity is unknown and cannot be calculated without more information. The given answer in the book is 36m/s, but the method used to obtain this answer is unclear. The relationship between the horizontal and vertical components of the velocity is also unknown.
  • #1
sakdjki
2
0

Homework Statement


A player hits a ball 45º above the horizontal 1.3m above the ground. It clears a 3m wall 130m away. What was the initial velocity?


Homework Equations


?


The Attempt at a Solution



Normally projectile motion problems don't give me much trouble, but in this instance I'm not given the initial velocity and hence I cannot find the horizontal or vertical components of the velocity. It is 45º, so my thought was to find an equation in which the v_x=v_y, but nothing comes to mind.

The answer in the book is supposedly 36m/s, working backwards gives me a horizontal/vertical velocity of 25.45m/s. I can find the total time of the trip and the total horizontal distance (at a height of 1.3m) but from there I am trumped to find anything remotely similar for the other equation.
 
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  • #2
Just had an epiphany

I think the 3m/130m height away is the vertex or maximum height

gonna try that out

edit: i don't think so... 100% stumped
 
Last edited:
  • #3


As a scientist, it is important to thoroughly understand the concepts and equations involved in a problem before attempting to solve it. In this case, the initial velocity can be found using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, due to gravity), and t is the time. Since the ball starts and ends at the same height, the vertical component of the velocity can be found using the equation s = ut + 1/2at^2, where s is the displacement (in this case, the height of the wall) and t is the time. With these two equations, the initial velocity can be solved for by setting the vertical component of the velocity equal to the final velocity (which is 0m/s at the top of the ball's arc). Once the initial vertical velocity is found, the horizontal component can be found using the equation v = u + at, where v is the final velocity (which is the same as the initial horizontal velocity), u is the initial velocity, a is the acceleration (in this case, 0m/s^2), and t is the time. By solving for t using the equation s = ut + 1/2at^2 and substituting it into the equation v = u + at, the initial horizontal velocity can be found. This approach may seem complex, but it is important to thoroughly understand the concepts and equations involved in order to accurately solve a difficult projectile motion problem.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is thrown, launched, or otherwise projected into the air and then moves freely under the influence of gravity.

2. What makes a projectile motion problem difficult?

A difficult projectile motion problem often involves multiple variables, non-uniform gravitational acceleration, and/or air resistance. These factors can make it challenging to accurately predict the trajectory and final position of the projectile.

3. How do you solve a difficult projectile motion problem?

To solve a difficult projectile motion problem, you must first identify all the known and unknown variables, such as initial velocity, angle of launch, and time. Then, you can use equations of motion, such as the kinematic equations, to calculate the unknown variables and determine the trajectory of the projectile.

4. What are some common mistakes to avoid when solving projectile motion problems?

Some common mistakes to avoid when solving projectile motion problems include forgetting to account for air resistance, using the wrong units for measurements, and rounding too early in the calculation process. It is also important to double-check your calculations and ensure they make logical sense.

5. How can understanding projectile motion be useful in real-life situations?

Understanding projectile motion can be useful in various real-life situations, such as predicting the trajectory of a ball in sports, calculating the range of a projectile launched from a military weapon, and designing roller coasters and other amusement park rides.

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