MULUNGUSHI UNIVERSITY
SCHOOL OF SCIENCE, ENGINEERING AND TECHNOLOGY
BACHELOR OF ENGINEERING IN MECHANICAL ENGINEERING
MEE 252 DYNAMICS 2022
ASSIGNMENT 1
INSTRUCTIONS:
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DUE DATE: FRIDAY APRIL 22 2022 BY 17: 00 HOURS
ANSWER ALL QUESTION
SUBMIT VIA MOODLE USING PDF FORMAT
QUESTION 1
(a) If the car shown in Figure Q1(a) decelerates uniformly along the curved road
from 25 m/s at A to 15 m/s at C, determine the acceleration of the car at B.
(10 marks)
Figure Q1 (a).
(b) The car shown in Figure Q1(b) travels up the hill with a speed of 𝑣 =
(0.2𝑠)𝑚/𝑠 here s is in meters, measured from A. Determine the magnitude of
its acceleration when it is at point s = 50 m, where 𝜌 = 500 𝑚 .
(10 Marks).
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Figure Q1 (b)
QUESTION 2
(a) The position of a particle is defined by 𝑟 = (𝑡 3 𝑖 + 3𝑗 + 8𝑡𝑘)𝑚, where t is in seconds.
Determine the magnitude of the velocity and acceleration and the radius of
curvature of the path when t = 2 s.
(12 Marks)
(b) The wheel shown in Fig Q3 rolls without slipping with an angular velocity of 𝜔 =
10 𝑟𝑎𝑑/𝑠 . Determine the magnitude of the velocity of point B at the instant shown.
(8 marks)
QUESTION 3
Figure Q2(b)
(a) The boat shown in Figure Q3(a) is traveling along the circular path with a speed
of 𝑣 = (0.0625𝑡 2 )𝑚/𝑠 , where t is in seconds. Determine the magnitude of its
velocity and acceleration when t = 10 s.
(10 Marks)
Figure Q3 (a)
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(b) The skateboard rider shown in Figure Q3 (b) leaves the ramp at A with an initial
velocity 𝑣𝐴 at a 30° angle. If he strikes the ground at B, determine 𝑣𝐴 and the
time of flight.
(10 Marks)
Figure Q3 (b)
QUESTION 4
(a) The velocity of the water jet discharging from the orifice can be obtained from 𝑣 =
√2𝑔ℎ where h = 2 m is the depth of the orifice from the free water surface as
shown in Figure Q4(a). Determine the time for a particle of water leaving the orifice
to reach point B and the horizontal distance x where it hits the surface. (8 Marks).
Figure Q4 (a)
(b) A projectile shown in Figure Q4 (b) is fired from the platform at B. The shooter fires
his gun from point A at an angle of 30°. Determine the muzzle speed of the bullet
if it hits the projectile at C.
(12 Marks)
Figure Q4(b)
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QUESTION 5
(a) Particle travels along a straight-line path y = 0.5x as shown in Figure Q5 (a) . If the x
component of the particle's velocity is 𝑣𝑥 = (2𝑡 2 ) m/s where t is in seconds,
determine the magnitude of the particle's displacement, velocity and acceleration
when t = 4 s.
(10 Marks)
Figure Q5 (a).
(b) The particle is traveling along the parabolic path 𝑦 = 0.25𝑥 2 shown in Figure Q5 (b). If
𝑥 = 2𝑡 2 m, where t is in seconds, determine the magnitude of the particle's velocity
and acceleration when t = 2 s.
(10 Marks)
Figure Q5 (b).
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