Projectile motion problem – determining initial velocity of throw

In summary, the initial velocity of the pitch can be found using the kinematic equation s = ut + 0.5 at^2, by first finding the time of flight of the baseball using horizontal components, and then substituting this value into the equation to solve for the initial velocity. The solution can be simplified by substituting t=18.5/(u*cos(2.5^o)) in both occurrences of t in the second (vertical) equation and solving directly for u. The answer given in the book is 45.2 m/s.
  • #1
Kaiser98
2
1
Homework Statement
A pitcher throws an overhand fastball from an approximate height of 2.65 m and at an
angle of 2.5° below horizontal. The catcher, catches the ball high in the strike zone, at a
height of 1.02 m above the ground. If pitcher's mound and home plate are 18.5 m apart,
what is the initial velocity of the pitch?
Relevant Equations
s = ut + 0.5 at^2

Answer given in book: 45.2 m/s
Screenshot 2022-11-28 at 4.11.00 AM.png


My reasoning was to use this kinematic equation to first get time of flight of the baseball using horizontal components, and then use this same equation again to find initial velocity.
 
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  • #2
Kaiser98 said:
Homework Statement:: A pitcher throws an overhand fastball from an approximate height of 2.65 m and at an
angle of 2.5° below horizontal. The catcher, catches the ball high in the strike zone, at a
height of 1.02 m above the ground. If pitcher's mound and home plate are 18.5 m apart,
what is the initial velocity of the pitch?
Relevant Equations:: s = ut + 0.5 at^2

Answer given in book: 45.2 m/s

View attachment 317812

My reasoning was to use this kinematic equation to first get time of flight of the baseball using horizontal components, and then use this same equation again to find initial velocity.
Hello @Kaiser98 .
:welcome:

You are inconsistent with your use of signs.

You have vertical distance the ball drops as being positive as well as acceleration due to gravity as being positive. That's all fine.
However, you have the angle below horizontal as being negative. Since you had been treating the downward direction as being positive for the other quantities, so should the 2.5° angle be positive.
 
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  • #3
Also, your solution uses unnecessary algebra and the more you do of that, the more you expose yourself to mistakes. Why not substitute ##t=18.5/(u\cos(2.5^o))## in both occurrences of ##t## in the second (vertical) equation and solve directly for ##u##?
 
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  • #4
I did what both of you said, and finally got the right answer. Thanks a lot!
 
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1. How do you calculate the initial velocity of a projectile?

The initial velocity of a projectile can be calculated using the equation v0 = (xf - x0) / t, where v0 is the initial velocity, xf is the final position, x0 is the initial position, and t is the time taken for the projectile to travel from the initial position to the final position.

2. What is the difference between initial velocity and final velocity?

Initial velocity refers to the velocity of a projectile at the moment it is launched, while final velocity refers to the velocity of the projectile at the moment it reaches its final position. Initial velocity is typically higher than final velocity due to the effects of gravity and air resistance.

3. How does the angle of projection affect the initial velocity of a projectile?

The angle of projection affects the initial velocity of a projectile by determining the vertical and horizontal components of the velocity. The initial velocity will be higher if the angle of projection is closer to 90 degrees, as this maximizes the vertical component of the velocity. However, the horizontal component will be higher if the angle of projection is closer to 0 degrees.

4. Can the initial velocity of a projectile be negative?

Yes, the initial velocity of a projectile can be negative if the projectile is launched in the opposite direction of the positive direction. This can happen if the projectile is thrown downwards or if the coordinate system is defined in a way that the positive direction is opposite to the direction of the throw.

5. How does air resistance affect the initial velocity of a projectile?

Air resistance can decrease the initial velocity of a projectile by exerting a force in the opposite direction of the projectile's motion. This force, known as drag, increases as the velocity of the projectile increases. Therefore, the higher the initial velocity, the greater the effect of air resistance on the projectile's motion.

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