Consider the motion of the following object. Assume the x-axis points east, the
ID: 1406005 • Letter: C
Question
Consider the motion of the following object. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the graviation force acts on the object unless otherwise stated.
b- make a sketch of the trajectory.
c- determine the time of flight and rang of the object.
d- determine the maximum height of the object.
A golf ball is hit east down a fairway with an initial velocity ( 50,0,30) m/s. A crosswind blowing to the south produces an acceleration of the ball of -0.8 m/s^2.
Explanation / Answer
initial velocity = vox = 50 m/s
voz = 30 m/s
voy = 0
acceleration due to gravity = az = -9.8 m/s^2
t
acceleration due to wind = ay = -0.8 m/s^2
part(a)
vx = = vox+ax*t = 50
vy = voy + ay*t = -0.8t
vz = voz + az*t = 30-9.8*t
x = xo + vox*t + 0.5*ax*t^2 = 50t
y = yo + voy*t + 0.5*ay*t^2 = 0.4*t^2
z = zo + voz*t + 0.5*az*t^2 = 30*t-4.9*t^2
part(c)
if z = 0
from z = 30*t-4.9*t^2
t = 4.9/30 = 0.163 s
after t time y = 0.4*0.163^2 = 0.01m
x = 50*0.163 = 8.15 m
range = sqrt(x^2+y^2) = 8.15 m
part(d)
if vz = 0
z = 30*0.163-4.9*0.163^2 = 4.75 m