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MCS702S - MECHANICS - 1ST OPP - NOV 2022 |
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n Am I BI A u n IVER s ITY
OF SCIEnCE
TECHnOLOGY
FACULTYOF HEALTH, NATURAL RESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 7
COURSE CODE: MCS702S
COURSE NAME: MECHANICS
SESSION: NOVEMBER 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS:82
EXAMINER
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
Prof A.S EEGUNJOBI; Ms K. DAVID
MODERATOR:
Prof O.D MAKIN DE
INSTRUCTIONS
1. Answer ALL questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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MCS702S
Iviechanics
November 2022
1. (a) A diver springs upward from a board that is 5.50m above the water. At the instant
he contacts the water his speed is 18.4 m/s and his body makes an angle of 64°
with respect to the horizontal surface of the water. Determine his
1. initial velocity
(4)
ii. magnitude
(3)
iii. and direction.
(3)
(b) A small object moves along the x-axis with acceleration ax(t) = -(0.032m/ s3)(15s-
t). At t = 0 the object is at x = -14m and has velocity Vax = 8m/ s. What is the
x- coordinate of the object when t = 10s?
(7)
2. (a) The position of a fly that is flying parallel to the ground is given as a function of
time by
f = (2.9m + (0.09m/ s2 )t2) i - (0.015m/ s3 )t3j
1. At what value of t does the velocity vector of the fly make an angle of 32°
clockwise from the +x-axis?
(5)
ii. At the time calculated in part (a), what are the magnitude and direction of the
fly's acceleration vector?
(5)
(b) A bird flies in the xy-plane with a velocity vector given by
The positive y-direction is vertically upward. At t = 0 the bird is at the origin.
1. Calculate the position and accelerationvectors of the bird as functions of time.
(5)
ii. What is the bird's altitude (y- coordinate) as it flies over x = 0 for the first
time after t = 0?
(3)
3. (a) You design a test gun that will accelerate chicken-sized objects, to study damage to
aircraft that collide with largebirds, so that their displacement along the gun barrel
is given by
x(t) = 9000t2m/ s2 - 80000t 3m/ s3 .
The object leaves the end of the barrel at t = 0.025s.
1. How long must the gun barrel be?
(4)
ii. Find the general solution of What will be the speed of the objects as they leave
the end ofthe barrel?
(4)
111. What net force must be exerted on a 1.50 kg object at
a) t = 0
(3)
(3) t = 0.025s
(3)
(b) An object of mass mis at rest in equilibrium at the origin. At t = 0 a new force
F'(t) is applied that has components
F'x= k1 + k2y F'(t) = k3t
where k1, k2 , and k3 are constants. Calculate the position f(t) and velocity iJ(t)
vectors as functions of time.
(6)
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MCS702S
Mechanics
November 2022
4. (a) An uncooperative cow is leaving the barn as you try harder and harder to push her
back in. In coordinates with the originat the barn door, the cow walks from x = 0
to x = 6.9m as you apply a force with x-component
Fx = -(20N + (3N /m)x.
How much work does the force you apply do on the cow during this displacement?
(6)
(b) A net force along the x-axis that has x-component Fx = -12N + (0.3N/m 4 )x2 is
applied to a 5 kg object that is initially at the origin and moving in the -x-direction
with a speed of 6m/ s. What is the speed of the object when it reaches the point
X = 5m?
(7)
5. A batter hits a baseball straight upward at home plate and the ball is caught 5.0 s after
it is struck in figure below.
(a) What is the initial velocity of the ball?
(3)
(b) What is the maximum height the ball reaches?
(3)
(c) How long does it take to reach the maximum height?
(3)
(d) What is the acceleration at the top of its path?
(2)
(e) What is the velocity of the ball when it is caught? Assume the ball is hit and caught
at the same location.
(3)
End of Exam!