No Dokumen: No Isu.
/Tarikh:
UNIVERSITI TEKNIKAL BMKT 2333
MALAYSIA MELAKA
Tajuk: TUTORIAL 1 – CHAPTER 1: No Semakan/Tarikh: Mukasurat:
KINEMATICS OF PARTICLES (Q) 1
1. A snowboarder starts from rest at the top of a double black diamond hill. As he rides down the
slope, GPS coordinates are used to determine his displacement as a function of time: x = 0.5t3 +
t2 + 2t where x and t are expressed in ft and seconds, respectively. Determine the position,
velocity, and acceleration of the boarder when t = 5 seconds. (Ans: x=97.5 ft, v=49.5 ft/s, a=17ft/s2)
2. The motion of a particle is defined by the relation x = t3 -12t2 +36t +30, where x and t are expressed
in feet and seconds, respectively. Determine the time, the position, and the acceleration of the
particle when v = 0. (Ans: t=2s, x1=62 ft, a1=-12 ft/s2 / t=6s, x2=30 ft, a2=12 ft/s2)
3. A baseball is thrown downward from a 50-ft tower with an initial speed of 18 ft/s. Determine the
speed at which it hits the ground and the time of travel. (Ans: v=59.5 ft/s, t=1.29s)
4. Traveling with an initial speed of 70 km/h, a car accelerates at 6000 km/h2 along a straight road.
How Jong will it take to reach a speed of 120 km/h? Also, through what distance does the car
travel during this time? (Ans: t=30s, s=792m)
5. If it takes 3s for a ball to strike the ground when it is released from rest, determine the height in
meters of the building from which it was released. Also, what is the velocity of the ball when it
strikes the ground? (Ans: h=44.1m, v=29.4m/s)
6. A group of students launches a model rocket in the vertical direction as shown in Figure 1. Based
on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the
powered portion of the flight and that the rocket landed 16 s later. Knowing that the descent
parachute failed to deploy so that the rocket fell freely to the ground after reaching its maximum
altitude and assuming that g =32.2 ft/s2, determine:
(a) the speed V1 of the rocket at the end of powered flight, (Ans: v=252 ft/s)
(b) the maximum altitude reached by the rocket. (Ans: Ymax=1076 ft)
Figure 1.
7. A volleyball player serves the ball with an initial velocity V0 of magnitude 13.40 m/s at an angle of
20° with the horizontal as shown in Figure 2. Determine
(a) if the ball will clear the top of the net, (Ans: Y=2.87m)
(b) how far from the net the ball will land. (Ans: 7.01m)
Figure 2.
8. A monorail train starts from rest on a curve of radius 400 m and accelerates at the constant rate
at. If the maximum total acceleration of the train must not exceed 1.5 m/s2, determine
(a) the shortest distance in which the train can reach a speed of 72 km/h, (Ans: x=178.9m)
(b) the corresponding constant rate of acceleration at. (Ans: at =1.118 m/s2)
9. The elevator shown in the figure moves downward with a constant velocity of 4 m/s as shown in
Figure 3. Determine:
(a) the velocity of the cable C, (Ans: vC=8.00m/s)
(b) the velocity of the counterweight W, (Ans: vW=4.00m/s)
(c) the relative velocity of the cable C with respect to the elevator, (Ans: vC/E=12.00m/s)
(d) the relative velocity of the counterweight W with respect to the elevator. (Ans: vW/E=8.00m/s)
Figure 3.
