Finding Initial Velocity and Angle in 2D Kinematics Problem

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Homework Help Overview

The problem involves a softball hit at an angle above the horizontal, with the third baseman running to catch it after a specified time. The goal is to find the initial velocity and angle of the ball using kinematic equations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the challenge of solving for multiple variables with limited known values, questioning how to derive the angle and initial velocity from the given equations.
  • Some participants suggest using the distance covered by the third baseman and the time to establish relationships between the variables.
  • There is exploration of the change in height and its implications for the equations used.
  • Participants attempt to manipulate the equations to isolate variables and express relationships between them.

Discussion Status

The discussion is ongoing, with participants actively engaging in deriving relationships between the variables. Some have offered hints and guidance on how to approach the equations, while others express confusion about the trigonometric aspects involved.

Contextual Notes

Participants note that the initial and final heights of the ball are the same, which is a critical assumption in the problem. There is also mention of the constraints of the homework context, including the need to work with the given time and distance.

CocoonOHorror
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Homework Statement



A softball is hit over a third baseman's head with some speed v-sub0 at an angle theta above the horizontal. Immediately after the ball is hit, the third baseman turns around and begins to run at a constant velocity V = 7.00m/s. He catches the ball t=2.00sec later at the same height at which it left the bat. The third baseman was originally standing L=18.0 m from the location at which the ball was hit. Find v-sub0 Use g=9.81 m/s^2 for the magnitude of the acceleration due to gravity. also find theta.

Homework Equations



x =( initial velocity times cos theta)* time
y = initial velocity times sin theta)* time - .5GT^2

The Attempt at a Solution



i don't understand how to solve an equation with 4 variables and i only have values for 2 of them. i have time = 2 seconds, and distance = 32 meters. how do i get an angle and an initial velocity?
 
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CocoonOHorror said:
i don't understand how to solve an equation with 4 variables and i only have values for 2 of them. i have time = 2 seconds, and distance = 32 meters. how do i get an angle and an initial velocity?
There are two equations and two unknowns. Hint: What's y, measured from the starting height?
 
is it 9.8 meters?
 
CocoonOHorror said:
is it 9.8 meters?
No. How does the initial height compare to the final height?
 
it seems like you just use the dude running at 7 m/s for 2 seconds to get the total distance (18m + 14m) but i guess that's not the right way to go about it?i really wish my physics prof spoke english!
 
Doc Al said:
No. How does the initial height compare to the final height?

they are the same.
 
CocoonOHorror said:
it seems like you just use the dude running at 7 m/s for 2 seconds to get the total distance (18m + 14m) but i guess that's not the right way to go about it?
No, that's perfectly correct. That gives you the value for x you'll need in the first equation.

What about y?
 
CocoonOHorror said:
they are the same.
Yes! So, if you measure from the starting point, what's y? (What's the change in height?)
 
Doc Al said:
Yes! So, if you measure from the starting point, what's y? (What's the change in height?)

zero?
 
  • #10
CocoonOHorror said:
zero?
Yes, y = 0 when t = 2.
 
  • #11
so i have:
32=(initial velocity*cos theta)*time
and
0= (initial velocity*sin theta)*time - .5GT^2
right?
but now what?
 
  • #12
wait, i have 16 = initial velocity * cos theta
and 9.8 = initial velocity * sin theta (or is it 4.9/2 = initial Velocity * sin theta ?)

(i think)
now what?
 
  • #13
Play around with those equations and see if you can isolate one of the variables. There are several ways to go. (Try division.)
 
  • #14
OK, maybe 16/cos theta = 9.8/sin theta?

im so lost...
 
  • #15
am i warm?
 
  • #16
is it an easy Trigonometric solution? I am in Trig/precalc algebra in one class and we just started the Trig half, so maybe I am not familiar with a function to equate Sin/Cos?
 
  • #17
CocoonOHorror said:
OK, maybe 16/cos theta = 9.8/sin theta?

im so lost...
You're not that lost. Multiply both sides by sin theta. (What other trig function appears?)
 
  • #18
does Tan theta = 9.8/16 ?
am i on the right track?
 
  • #19
holy mackeral! thanks Doc Al, i really appreciate the help!
 
  • #20
You got it. :approve:
 

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