Physics 121H
Fall 2015
Homework #3
31-August-2015
Due Date : 9-September-2015
Reading :
Chapter 4
Reminders:
The calculus quiz will be at the beginning of the Mon. 31-Aug-2015
sesssion. The calculus review and solutions can be found on the class web
page. The vector quiz will be at the beginning of the Wed. 9-Sep-2015
session. The vector review and solutions can be found on the class web
page.
1. You stand atop a building and throw a ball so that it leaves your hand with speed vo a
distance h above flat ground. Find the difference in the horizontal displacement of the
ball if you throw it so that it makes an initial angle of θo or -θo with respect to horizontal.
2. An electron is launched from the lefthand edge of the bottom of 2 parallel
metal plates. Its initial velocity has
magnitude vo and makes an angle θo
relative to the plane of the plate. The
plates are a distance D long and are
separated by a distance H, as shown. While it is in between the plates, the electron
experiences a constant downward acceleration with magnitude a. (a) Assuming that the
electron does not strike the upper plate, find the smallest value of vo so that the electron
does not strike the lower plate. (b) For the value of vo found in (a), find the smallest
value of H so that the electron does not strike the upper plate. (c) For values of H larger
than that found in (b), find the range of initial speeds, vo, so that the electron does not
strike either plate.
3. In the picture, a lump of wet putty moves in uniform
circular motion as it rides at a radius of 20.0 cm on the
rim of a wheel rotating counter clockwise with a period
of 5.00 ms. The lump then happens to fly off the rim at
the 5 o'clock position (as if on a clock face). It leaves the
rim at a height of h = 1.20 m from the floor and at a
distance d = 2.50 m from a wall. At what height on the
wall does the lump hit?
4. The minute hand of a wall clock measures 10 cm from its tip to the axis about which it
rotates. The magnitude and angle of the displacement vector of the tip are to be
determined for three time intervals. What are the (a) magnitude and (b) angle from a
quarter after the hour to half past, the (c) magnitude and (d) angle for the next half hour,
and the (e) magnitude and (f) angle for the hour after that?
!
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5. The acceleration of a particle moving only on a horizontal xy plane is given by
r
r
a = 3t iˆ + 4t ˆj , where a is in meters per second-squared and t is in seconds. At t=0, the
r
position vector r = (20.0 m) iˆ + (40.0 m) ˆj locates the particle, which then has the
r
velocity vector v = (5.00 m/s) iˆ + (2.00 m/s) ˆj . At t= 4.00 s, what are (a) its position
vector
notation and (b) the angle between its direction of travel and the
!
! in unit-vector
positive
the x axis?
! direction of!
!
!
!
! the line y = 30 m with a
6. In the figure, particle A moves along
r
constant velocity v of magnitude 3.0 m/s and parallel to the x
axis. At the instant particle A passes the y axis, particle B leaves
r
the origin with zero initial speed and constant acceleration a of
r
magnitude 0.40 m/s2. What angle θ between a and the positive
!
direction of the y axis would result in a collision?
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7. A projectile’s launch speed is 5 times its speed at maximum height. Find the launch
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angle, θo.
8. A ball rolls off of the top step of a staircase moving with speed
vo. Each step is L wide and L high. Which step does the ball hit
first?
9. Suppose that a space probe can withstand the stresses of a 20g acceleration.
(a) What is the minimum turning radius of such a craft moving at a speed of one-tenth the
speed of light? (b) How long would it take to complete a 90° turn at this speed?
10. A cat rides a merry-go-round turning with uniform circular motion. At time t1=2.00 s,
r
the cat's velocity is v1 = (3.00 m/s) iˆ + (4.00 m/s) ˆj , measured on a horizontal x-y
r
coordinate system. At t2=5.00 s, its velocity is v2 = (-3.00 m/s) iˆ + (-4.00 m/s) ˆj . What
are (a) the magnitude of the cat's centripetal acceleration and (b) the cat's average
acceleration during the time
t1, which is less than one period?
! interval t2 – !
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