Kinematics Problem: How Far Will a Pitch Fall Vertically at 61.2 ft?

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SUMMARY

The discussion centers on a kinematics problem involving the vertical drop of a baseball pitch thrown horizontally at 100.8 mi/hr, specifically how far it falls over a distance of 61.2 ft. The initial calculations converted the speed to 147.84 ft/s and determined the time to travel 61.2 ft as approximately 0.414 seconds. Using the equation y = 0 + (0)(0.41396) + (1/2)(-9.8)(0.41396)^2, the calculated drop was -0.8934 ft. However, this result contradicts the expected range of 1.8 to 3.6 ft, prompting a reevaluation of the gravitational constant used in the calculations.

PREREQUISITES
  • Understanding of basic kinematics equations, specifically the equation of motion: x = x_0 + v_0 t + (1/2) a t^2
  • Knowledge of unit conversions, particularly from miles per hour to feet per second
  • Familiarity with gravitational acceleration values in different units (ft/s² vs. m/s²)
  • Basic problem-solving skills in physics
NEXT STEPS
  • Review the correct value of gravitational acceleration in feet per second squared for kinematics problems
  • Practice additional kinematics problems involving horizontal motion and vertical drop
  • Learn about projectile motion and its equations in physics
  • Explore the impact of air resistance on projectile motion in real-world scenarios
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and projectile motion, as well as educators seeking to clarify concepts related to horizontal and vertical motion in real-world applications.

Xaran
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Homework Statement


Directly from my homework.

One of the fastest recorded pitches in major-league baseball, thrown by Nolan Ryan in 1974, was clocked at 100.8 mi/hr. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached 61.2 ft away?

It wants the answer in ft.

Homework Equations


LaTeX Code: x = x_0 + v_0 t + (1/2) a t^2


The Attempt at a Solution



I started by converting mi/hr to ft/s and got 147.84 ft/s. So with this I figured that the ball would travel the 61.2 ft in 0.41396 seconds. From there I plugged it into the relevant equation to get y = 0 + (0)(0.41396) + (1/2) (-9.8) (0.41396)^2 to get an answer of -0.8934 ft.

The problem is that my question comes with an answer range that says my answer should fall somewhere between 1.8 and 3.6 ft. I've checked and double-checked the problem and I thought I've done it right, but I wanted to get a second opinion. Did I do the problem correctly and the answer range is just wrong, or am I missing something?
 
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Xaran said:

Homework Statement


Directly from my homework.

One of the fastest recorded pitches in major-league baseball, thrown by Nolan Ryan in 1974, was clocked at 100.8 mi/hr. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached 61.2 ft away?

It wants the answer in ft.

Homework Equations


LaTeX Code: x = x_0 + v_0 t + (1/2) a t^2

The Attempt at a Solution



I started by converting mi/hr to ft/s and got 147.84 ft/s. So with this I figured that the ball would travel the 61.2 ft in 0.41396 seconds. From there I plugged it into the relevant equation to get y = 0 + (0)(0.41396) + (1/2) (-9.8) (0.41396)^2 to get an answer of -0.8934 ft.

The problem is that my question comes with an answer range that says my answer should fall somewhere between 1.8 and 3.6 ft. I've checked and double-checked the problem and I thought I've done it right, but I wanted to get a second opinion. Did I do the problem correctly and the answer range is just wrong, or am I missing something?

Welcome to PF.

Shouldn't you be using a different value for gravity in ft/s2
 
And there's the small detail I overlooked. Its always something simple. Thanks! And thanks for the welcome. Just started my physics class this semester, so sometimes the little things like that escape me.
 

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