PHY 2053, Fall 2009, Quiz 2 — Whiting
1. A person takes a trip, driving with a constant speed of 90.0 km/hr, except for a 15.0-min
rest stop. If the person’s average speed is 60.0 km/hr,
a) How much time is spent on the trip?
Let t be the total time for the trip (in hr), and let x be the total distamce travelled (in km).
Then:
x = 60.0 × t = 90.0 × (t − 0.250) =⇒ t =
90.0 × 0.250
= 0.750 hr = 45.0 min .
30.0
b) How far does the person travel?
t=
x
60.0 × 90.0
x
=
+ 0.250 =⇒ x = 0.250 ×
= 45.0 km
60.0
90.0
(90.0 − 60.0)
2. Runner A is initially 6.00 km west of a flagpole and is running with a constant velocity of
4.00 km/hr due east. Runner B is initially 5.00 km east of the flagpole and is running with
a constant velocity of 3.00 km/hr due west.
a) How long will it take before the runners meet?
After time t, xA = −6.00 + 4.00 × t, and xB = 5.00 − 3.00 × t. When they meet (at tmeet ),
xA = xB , i.e., xA = −6.00 + 4.00 × tmeet = 5.00 − 3.00 × tmeet = xB .
=⇒ tmeet = 11.00/7.00 hr = 1.57 hr.
b) How far are they from the flagpole when they meet?
Consider the time it takes each to reach the position x.
tA =
x − (−6.00)
,
4.00
tB =
x − 5.00
.
(−3.00)
When they meet (at xmeet ), tA = tB . Thus:
tA =
xmeet − 5.00
1
1
5.00 6.00
xmeet − (−6.00)
=
= tB =⇒ (
+
) × xmeet =
−
,
4.00
(−3.00)
3.00 4.00
3.00 4.00
i .e., xmeet =
2.00
km = 0.286 km.
7.00