Velocity and height of a ball thrown at an angle

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Homework Help Overview

The problem involves a baseball batted at an angle of 35 degrees above the horizontal, which is caught 390 feet away at the same height from which it was hit. The original poster seeks to determine the initial speed of the ball and the maximum height it reaches above the point of contact with the bat.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use equations related to distance and angle but expresses uncertainty about the correct equations. Some participants question the units used for angles and suggest clarifying the terminology related to horizontal distance. Others propose focusing on the initial speed of the ball and the relevant equations for projectile motion.

Discussion Status

Participants are actively discussing the problem, with some providing guidance on the importance of unit consistency and the correct application of the range equation. There is no explicit consensus yet, but the conversation is exploring various interpretations and approaches to the problem.

Contextual Notes

There is a noted confusion regarding the units of angles and the necessity of converting distances into consistent units for calculations. The original poster's attempts to apply equations without addressing these unit issues are highlighted as a potential source of error.

enantiomer1
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Homework Statement


A batted baseball leaves the bat at an angle of 35.0 degrees celsius above the horizontal and is caught by an outfielder 390 ft from home plate at the same height from which it left the bat. what was the initial speed of the ball and How high does the ball rise above the point where it struck the bat?

Homework Equations


D= v0t
D= v0sin 35 degrees

The Attempt at a Solution


I tried to figure it out using both the equations, but I guess I must be doing something wrong, does anyone know what equation I'm not using?
 
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First, angles do not have units in degrees celsius; angles can be in degrees or radians. You probably had a mind slip, right? =)

Second, the equations that you posted aren't useful right now, but they could be later depending on your problem-solving approach.

Let's work on the first listed unknown, the initial speed of the ball. What is the given data? We know the given angle (35 degrees), and we know that total horizontal distance the ball travels (390 feet--don't forget to convert to meters, if the answer requires it). The ball initially leaves the bat at some height that is unknown, but we do know that the ball is caught at exactly this same height. There is a specialized term to describe such a horizontal distance. What is this term? Do you have any equations for such motion that use this term?
 
The equation I was looking for is v0= sqrt(R[which in this case is just x]*g/sin(2 theta).
However everytime I plug it in I get sqrt(390*9.81/sin(70))= 63.81 ft/s, converted to m/s this is 63.81 ft/s * .3048 = 19.45 and this is STILL wrong... what am I not adding?
 
Yes, as you have demonstrated, you want to use the range equation here.

Your problem is that you did not covert 390 ft into meters first. Notice that you have 390 * 9.81; 390 is in units of feet and 9.81 is in units of "meters" per second-squared. Your mixing the length units.
 

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