CURVILINEAR MOTION
• If the direction of the resultant passing the
center of gravity of the body is varying, the
motion path will be a curved line called
curvilinear translation.
• It is often convenient to study these kinds
of motion by resolving each parameter in its
components.
PROJECTILE MOTION
• The equation developed in the
discussions for Rectilinear and Uniformly
Accelerated Rectilinear Motion (free-fall)
will be used in the analysis of the motion
of projectile.
• The actual motion of projectile is
influenced by a number of factors, such as
the rotation of the projectile due to the
rifling of the barrel, wind velocity, humidity,
etc., which require modifications in the
results found from the assumed ideal
conditions. The motion of a projectile
moving without rotation in a vacuum will
here be considered.
Velocity in Curvilinear motion
Acceleration in Curvilinear motion
Vector Representation
Trajectory – the path of the projectile.
Range – the total distance covered by the
projectile during the time of flight.
Time of flight – the time from the launch of
the projectile to its landing on the ground.
Sample Problem #1 At time t = 10 s, the velocity of a particle moving in the
x-y plane is v = 0.1i + 2j m/s. By time t = 10.1 s, its velocity has become −0.1i
+ 1.8j m/s. Determine the magnitude (aave) of its average acceleration
during this interval and the angle made by the average acceleration with the
positive x-axis.
Sample Problem #2 For a certain interval of motion the pin A is forced to
move in the fixed parabolic slot by the horizontal slotted arm which is
elevated in the y-direction at the constant rate of 3 in. /sec. All
measurements are in inches and seconds. Calculate the velocity v and
acceleration a of pin A when x = 6 in.
Sample Problem #3 A team of engineering students designs a medium size
catapult which launches 8-lb steel spheres. The launch speed is v0 = 80
ft/sec, the launch angle is = 35° above the horizontal, and the launch
position is 6 ft above ground level. The students use an athletic field with an
adjoining slope topped by an 8-ft fence as shown.
Determine:
(a) the time duration tƒ of the flight
(b) the x-y coordinates of the point of first impact
(c) the maximum height h above the horizontal field attained by the ball
(d) the velocity (expressed as a vector) with which the projectile strikes the
ground (or the fence)
Sample Problem #4 A boy tosses a ball onto the roof of a house. For the
launch conditions shown, determine the slant distance s to the point of
impact. Also, determine the angle which the velocity of the ball makes with
the roof at the moment of impact.
Sample Problem #5 The pilot of an airplane carrying a package of mail to a
remote outpost wishes to release the package at the right moment to hit the
recovery location A. What angle with the horizontal should the pilot’s line of
sight to the target make at the instant of release? The airplane is flying
horizontally at an altitude of 100 m with a velocity of 200 km/h.