TA: Tomoyuki Nakayama
Monday, September 20, 2010
PHY 2048: Physic 1, Discussion Section 0132H
Quiz 3 (Homework Set #4)
Name:
UFID:
Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator.
You need to show all of your work for full credit.
________________________________________________________________________________
In the overhead view of the figure below right, Jeeps P and B race along straight lines, across flat
terrain, and past stationary border guard A. Relative to the guard, P travels at a constant speed of
20.0 m/s, at the angle θ1 = 55.0º. Relative to the guard, B has accelerated from rest at a constant rate
of 0.500 m/s2 at the angle θ2 = 25.0º. At a certain time during the acceleration, B has a speed of 30.0
m/s.
a) At that time, what are the magnitude and
direction of the velocity of P relative to B?
We take our +x axis to the east and +y axis to
the north. In unit-vector notation, the velocity of
P with respect to stationary guard A is
vPA = 20cosθ1i + 20sinθ1j = 11.5i + 16.4j
The velocity of B with respect to A is
vBA = 30cosθ2i + 30sinθ2j = 27.2i + 12.7j
The velocity of P relative to B is
vPB = vPA – vBA = -15.7i + 3.7j
The magnitude of vPB is
vPB = √((-15.7)2+3.72) = 16.1 m/s.
The direction is
θ = tan-1(3.7/(-15.7)) = -13.3 + 180 = 167º, 13º north of west.
Note that vPB has a negative x component and positive y component, so it is in the 2nd quadrant.
b) At that time, what are the magnitude and velocity of the acceleration of B relative to P?
Since P moves at a constant velocity, its acceleration is zero. Thus we have
aBP = aBA – aPA = aBA
It has a magnitude of 0.500 m/s2 and is directed 25º north of east.