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Physics 104

Review - Two Dimensional Motion


An object experiences displacements s1 ands2, as shown in Fig. 1a above.  Is the resultant displacement s shown in Fig. 1b or Fig. 1c? Explain your answer.


Show how two displacement vectors, one of magnitude 6 m and the other of magnitude 8 m, can be combined to give a resultant of  (a) 2 m,  (b) 14 m, and (c) 10 m.


Vector A has magnitude 10 cm and makes an angle of 37o with the x-axis. Vector B has components Bx = 8 cm and By = -2 cm. Sketch the vector
C = A + 1/2 B and determine its components, its magnitude, and the angle it makes with the X-axis.


A particle moves 7.00 m along the positive Y-axis and then 7.07 m at angle of 450 with the X-axis, as shown in Fig. 2 below. Find the resultant displacement r = r1 + r2 of the particle. Express r in terms of (a) unit vectors i and j and (b) its magnitude and direction.


A pitcher throws a baseball with a horizontal velocity of 132 ft/s (90 mph) toward home plate that is approximately 60 ft away. What is the vertical drop of the ball when it reaches the plate? g = 32 ft/s2.


A young man practicing his pitching stands on a cliff and tosses a rock at a velocity of 24 m/s in a horizontal direction. At this instant a person in a car at rest in a service station 90 m from the cliff "guns" the car at a constant acceleration of 4.0 m/s2 toward the cliff. The rock hits the car. (a) How long is the rock in the air? (b) How high is the cliff?


A ball rolls off the edge of a 1.0 m-high table with a speed of 4.0 m/s. How far horizontally from the edge of the table does the ball strike the floor?


When an object is given an initial velocity vox along a horizontal frictionless surface, it travels a distance x = voxt in time t.

When an object is given an initial velocity vertically upward of voy from an initial height yo, it rises until its velocity vy = 0.

The maximum height ymax it rises can be found from
0 = vy2 = voy2 + 2ay(ymax - yo),
where ay = -9.8 m/s2 » 10 m/s2.

The time t it is in the air is found when
y = 0 = yo + voyt + 1/2 ayt2.
The velocity at this time t is given by
vy(t) = voy + ayt.
The principle of superposition states that when a body is subjected to two or more separate influences it responds to each without altering its response to the other. If the object is given an initial velocity of vo at angle Θ such that the components of its velocity are the same vox and voy as given above, what happens to the quantities t, ymax, vy(t), and x?


Find and draw the horizontal and vertical components of the projectile's velocity in Fig. 3 (a) below at the initial position i, (b) at the highest point h, and (c) just before it hits the ground at f.  (d) Draw the velocity vector at h and f.  (e) Draw the acceleration vectors for x = 20.0, 30.0 and 40.0 m.


An object is shot into the air with an initial velocity vo = 25 m/s at an angle of 370 above the horizontal at a height of 20 m above the earth's surface (Fig. 4 below).  Take g = 10 m/s2.  Find and draw the horizontal and vertical components of the projectile's velocity in Fig. 4 (a) at the initial position, (b) at the highest point. Find (c) the maximum height ymax to which the object rises, (d) the time for it to return to the earth, (e) the distance moved horizontally, and (f) draw the horizontal and vertical components of the velocity just before it hits the ground.  (g) Draw the velocity vector just before it hits the ground and find its magnitude and direction.


A boy throws a ball into the air as hard as he can and then runs as fast as he can under the ball in order to catch it. If his maximum speed in throwing the ball is 20 m/s and his best time for a 20-m dash is 3.0 s, how high does the ball rise. Take g = 10 m/s2.


A driven golf ball just clears the top of a tree that is 15 m high and is 30 m from the tee, and then lands (with no roll or bounce) on the green, 180 m from the tee. What was the initial velocity imparted to the golf ball? Take g = 10 m/s2.


A small object of mass m rotates counterclockwise on a horizontal frictionless plane at the end of a string of length r = 0.4 m with constant speed v = 2.0 m/s. On Fig. 6 draw the magnitude and direction of (a) the velocity and (b) the centripetal acceleration at points A, B, and C. Are (c) the velocity and (d) the acceleration constant? (d) Could you use this method to find how many “g’s” this object could withstand. Explain your answers.


(a) The period T of an object moving with uniform circular motion is defined as the time for one complete rotation. Find the period for the particle in #13.
(b) The frequency f of an object is defined as the number of rotations it makes per second. Find the frequency of the particle in #13. How is the frequency related to the period? Write an expression for the centripetal acceleration in terms of (c) π, r, and T,  (d) π, r, and f.

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Susan D. Kunk
Phyllis J. Fleming
September 25, 2002
April 2, 2003