PY1007 Study Problems – Week 4
Projectile Motion, Circular Motion, Simple Pendulum
Tutorial on 30th September
(1) A dart is thrown horizontally with an initial speed of 10 m/s toward the bull’s eye
on a dart board. It hits at a point directly below the bull’s eye 0.19 s later. (a) How
far below the bull’s eye does the dart hit? (b) How far away from the dart board was
the dart thrown?
Answers: (a) 0.18 m; (b) 1.9 m
(2) A supply airplane diving at an angle of 35.0◦ with the horizontal releases a package
of supplies at an altitude of 130 m. The package hits the ground 3.50 s after being
released. (a) What is the speed of the plane? (b) How far did the package travel
horizontally during its flight?
Answers: (a) 122 m/s; (b) 350 m
(3) On a French TGV train, the magnitude of the acceleration experienced by the
passengers is to be limited to 0.050g. (a) If such a train is going around a curve at a
speed of 216 km/hr what is the smallest radius of curvature that the curve can have
without exceeding the maximum allowed acceleration on the passengers? (b) What
is the maximum speed with which the train can go around a curve with a 1.00 km
radius, if the acceleration exerted on the passengers is not to exceed its maximum
allowed value?
Answers: (a) 7.35 km; (b) 22.1 m/s
40
(4) An airplane is flying in a horizontal circle at a speed of 480 km/hr. If its wings
are tilted 40◦ to the horizontal, what is the radius of the circle in which the plane is
flying? Assume that the required force is provided by a lift force that is perpendicular
to the wing surface.
Answer: 2.15 × 103 m
(5) A simple pendulum of length 1.20 m is drawn aside an angle of 6.0◦ with the
vertical and is then released, so that it swings back and forth. The mass of the
bob is 300 g. Determine (a) the period and angular frequency of the oscillations.
(b) Determine the maximum displacement smax of the bob away from the central
position along the circular arc along which it travels. (c) Write expressions for the
displacement and velocity of the bob as a function of time, taking t = 0 to be the
time the bob is released. (d) Find the speed and centripetal acceleration of the bob
when it is passing through the central position. (e) Find the tension in the string
when the bob is passing through the central position.
Answers: (a) 0.350 s, 18.0 rad/s; (b) 0.126 m; (c) s = smax cos ωt, v = −smax ω sin ωt;
(d) 2.27 m/s, 4.29 m/s; (e) 4.23 N