Faculty of EMS
Mechatronics Department
Mechanics II
Prof. Dr. Imam Morgan
Assignment (1)
Due Date: Thursday 27th of February 2025
Note: Kindly submit the assignment in the given format.
-1-
Problem (1):
The motion of a particle is defined by the relation
𝑥 = 𝑡 4 − 19𝑡 3 + 78𝑡 2 − 112𝑡 + 10
where x and t are expressed in millimeters and seconds, respectively. Determine:
(a) When the velocity is zero,
(b) the displacement, total distance traveled, average velocity during the time
interval 0 ≤ t ≤ 10 seconds. Sketch the motion during the mentioned interval.
-2-
Problem (2):
The acceleration of point A is defined by the relation
𝑎 = −1.8 sin(𝑘𝑥), where 𝑎 and 𝑥 are expressed in
m/s2 and meters, respectively, and k = 3 rad/m.
Knowing that 𝑥 = 0 and 𝑣 = 0.6 m/s when 𝑡 = 0,
determine the following:
(a) The symbolic equation of the velocity.
(b) Position of point A when 𝑣 = 0.
-3-
Problem (3):
Block A moves down with a constant velocity of 2 m/s.
Determine:
(a) The velocity of block C.
(b) The velocity of collar B relative to block A.
(c) The relative velocity portion D of the cable with
respect to block A.
-4-
Problem (4):
A ski jumper starts with a horizontal take-off velocity of 25 m/s and lands on a
straight landing hill inclined at 30 degrees. Determine:
(a) The time between take-off
25 m/s
and landing.
(b) The length 𝑑 of the jump.
(c) The maximum vertical
distance between the
jumper and the landing
hill.
-5-
Problem (5):
A golfer hits a ball with an initial velocity of 𝑣0 at an angle α with the horizontal.
Knowing that the ball must clear the tops of two trees and land as close as possible
to the flag, determine α given that 𝑣0 = 38 m/s and 𝑑 = 2.75 m.
-6-
Problem (6):
The car is traveling at a speed of 95 km/h as it approaches point A. Beginning at A,
the car decelerates at a constant rate of 2 m/s2 until it gets to point B, after which its
constant rate of decrease of speed is 0.9 m/s2 as it rounds the interchange ramp.
Determine the magnitude of the total car acceleration:
a) just before it gets to B,
b) just after it passes B, and
c) at point C.
-7-
Problem (7):
After taking off, a helicopter climbs in a straight line at a constant angle β. Its
flight is tracked by a radar from appoint A. Determine:
(a) The speed of the
helicopter in terms of d,
β, θ and 𝜃̇.
(b) The tangential and
normal acceleration of
the helicopter in terms of
d, β, θ, 𝜃̇ and 𝜃̈.
-8-
Problem (8):
As the hydraulic cylinder rotates around O,
the exposed length l of the piston rod is
controlled by the action of oil pressure in the
cylinder. The cylinder rotates at the constant
rate 𝜃̇ = (π/3) rad/s and l is decreasing at the
constant rate of 𝑟̇ =150 mm/s.
a) Calculate the velocity v of end B.
b) Calculate the acceleration a of end B.
-9-