Posted by Cheryl | Posted in Golf Tees | Posted on 16-05-2009
Tags: golf, golf tee heights, height, science_project, tee, tee_height

A 49.8-g golf ball is driven from the tee with an initial speed of 49.8 m/s and rises to a height of 24.5 m. (
A 49.8-g golf ball is driven from the tee with an initial speed of 49.8 m/s and rises to a height of 24.5 m. (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) What is its speed when it is 5.62 m below its highest point?
let us treat the trajectory of ball as that of projectile
initial speed = u = 49.8 m/s
angle of flight from horizontal = θ
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with these parameters, the highest point is given by
h = 24.5 m = u^2 sin^2 θ/2g
u^2 sin^2 θ = 2g h(max)
—————————-
the speed of the ball>> components at highest point
vx = u cos θ >> vy = 0
KE of ball (at h-max) = 0.5*m*(u^2 cos^2 θ)
= 0.5*m*[u^2 - u^2 sin^2 θ]
= 0.5*m*[u^2 - 2g h-max]
= 0.5*49.8*10^-3*[49.8^2 - 2*9.8*24.5]
KE of ball (at h-max) = 49.8 Joule
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what a coincidence on numerical values
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b) let at desired point y= 5.62 m on trajectory the angle of speed (v) be (p)
then vx = v cos p = u cos θ
vy= v sin p = u sin θ – gt
squaring & adding
v^2 = u^2 – 2ugt sin θ + g^2t^2
v^2 = u^2 – 2g[u sin θ*t + 0.5 gt^2]
v^2 = u^2 – 2g[y]
v^2 = 49.8^2 – 2*9.8[5.62] = 2369.888
v = 48.68 m/s
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