ME 218  ENGINEERING COMPUTATIONAL METHODS
Homework # 2
Assigned: September 8
th
, 2011
Due: September 15
th
, 2011
Name: _____________________
UT EID: _______
Section Unique Number: _________________
Problem 1
Trajectory of a ball is defined in the (x,y) coordinates. The trajectory can be
modeled using the equation below (the picture on the right hand side illustrates
the problem)
࠵
=
࠵
∙
tan
࠵
!
−
!
!
!
!
!
!"#
!
!
!
࠵
!
+
࠵
!
The thrower’s ball leaves the hand at an elevation
࠵
!
=
2 m, with initial velocity
࠵
!
=
20
m/s and the distance to the catches is
࠵
=35 m. You can assume that the
gravity acceleration is
࠵
=
9
.
81
m/s
2
. We need to determine at what angle
࠵
!
should the ball be released.
(a) Initial guess for the interval within which this initial angle must be have
been selected to be 0 and
࠵
/
2
radians. Can you perhaps explain the
thinking behind this selection of the values for the angle that bracket the
actual value of the angle?
(b) Perform 3 iterations of the bisection method. Report only 2 decimal digits.
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