Projectile Motion

  • Thread starter jazz20
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Homework Statement


the center field fence in a ball park is 10ft high and 400 feet from home plate. the ball is hit 3 ft above ground. it leaves the bat at an angle of theta degrees with the horizontal speed of 147.67ft/second. find the minimum angle at which the ball must leave the bat in order for hit to be a home run.
the path of the projectile is modeled by the parametric equations:
x=v0cos(theta)t
y=3+(v0sin(theta)t-15t^2

Homework Equations





The Attempt at a Solution


substitute 400 in for x and 147.67 for v0to solve for t
t=400/(146.67cos(theta)
then i took t and put it into the equation for y
y=3+(147.67sin(theta)(400/(146.67cos(theta))-16(400/(146.67cos(theta))^2


Did I do this correctly? If so, can some one help me with the math to solve for theta?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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The Attempt at a Solution


substitute 400 in for x and 147.67 for v0to solve for t
t=400/(146.67cos(theta)
then i took t and put it into the equation for y
y=3+(147.67sin(theta)(400/(146.67cos(theta))-16(400/(146.67cos(theta))^2


You can rewrite the equation as
y = 3 + 400*tanθ - 16*400^2*sec^2θ/146.67^2 [ 1/cosθ = secθ]
Put sec^2θ = 1 + tan^2θ,and solve the quadratic for tanθ.
 

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