Workbook Chapter 4b: Projectile Motion
Physical and Conceptual issues

Chapter 4 Newton's Laws of Motion Force and Velocity Vectors

1. Draw sample vectors to represent the force of gravity on the ball in the positions shown above (after it leaves the thrower's hand). Neglect air drag.

2. Draw sample bold vectors to represent the velocity of the ball in the positions shown above. With lighter vectors, show the horizontal and vertical components of velocity for each position. Neglect air drag.

3. (a) Which velocity component in the previous question remains constant? Why?

(b) Which velocity component changes along the path? Why?

4. It is important to distinguish between force and velocity vectors. Force vectors combine with other force vectors, and velocity vectors combine with other velocity vectors. Do velocity vectors combine with force vectors?________

5. Neglecting friction, all forces on the bowling ball, weight down and support of alley up, are shown on the ball before it strikes the pin (a). Draw vectors of all the forces that act on the ball (b) when it strikes the pin, and (c) after it strikes the pin.

Projectile Motion and Initial Velocity

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The initial velocity of several projectiles are listed below. For each case, determine the initial x and y velocity components and the velocity components two seconds after the projectile was launched. Assume g = 10m/s2 and ignore air resistance.

Initial velocity	vo(0 s)	vx (2 s)	voy (0 s)	vy (2 s)
(a) 50 m/s 37û above horizontal
(b) 50 m/s 30û above horizontal
(c) 50 m/s horizontally
(d) 50 m/s 30û below horizontal
(e) 50 m/s 37û below horizontal

(f) At what time does projectile (a), described above, reach its highest point?

(g) What is the velocity (magnitude and direction) of projectile (a) at that point?
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The components of the initial velocity for several projectiles are given below. Determine the magnitude and direction of the initial velocity.

	v ox(m/s)	v oy (m/s)	v o (m/s)	Direction
(h)	10	20
(i)	20	10
(j)	20	&endash;10

Kinematic Equations of Motion for Projectiles

Horizontal Direction	Vertical Direction (if UP is positive)
x = voxDt	y = -.5g Dt2 + voy Dt + yo
	vy = -g Dt + voy

Distance a dropped object falls in time interval D t = ?

ALPS Kits I - 33

Mathematical Aspects

Conceptual and physical aspects are essential, and the best way to begin a study of projectile motion. However, projectile motion problems can appear to be a vast array of "types" of problems to learn, unless you get mathematical!

So how many different ways are there to slice this apple, really? How many numbers in each of the following problems?

A surfaced submarine at position r = 3000 i + 800 j m fires a torpedo at 85 m/s in an attempt to hit a destroyer currently at r= 5000 i -600 j m and travelling with v = 15 i + 6 j m/s. The torpedo scores a direct hit.

Motion Diagram:

Motion Graphs: (Use solid lines for X, dashed lines for Y. Distinguish between the torpedo and the destroyer.)

A surfaced submarine at position r = 3000 i + 800 j m fires a torpedo at 85 m/s in an attempt to hit a destroyer currently at r= 5000 i -600 j m and travelling with v = 15 i + 6 j m/s. The torpedo scores a direct hit.

Free Algebra tip: Use sin² u + cos² u =1 to eliminate u from the two equations.

Motion Information:

TORPEDO

Event 1 =		Event 2 =
t1 =		t2 =
x1 = y1 =		x2 = y2 =
vx1 = vy1 =		vx2 = vy2 =
	ax12 = ay12 =

DESTROYER

Event 1 =		Event 2 =
t1 =		t2 =
x1 = y1 =		x2 = y2 =
vx1 = vy1 =		vx2 = vy2 =
	ax12 = ay12 =

A space probe travelling at v = 1.5 x 10³ i - 2.1 x 10² j + 4.5 x 10⁴ k m/s at r = 1.0 x 10¹¹ i + 6.1 x 10⁶ j + 4.5 x 10¹² k m (with respect to mission control) spots an enemy space station. The space station is travelling at v = 1.9 x 10³ i - 2.1 x 10² j + 4.5 x 10⁴ k m/s at r = 1.0 x 10¹¹ i + 6.7 x 10⁶ j + 4.5 x 10¹² k m (with respect to mission control). The space probe attempts to 'tag' the space station by attaching to it a tracking device. The space probe launches the tracking device at 500 m/s (with respect to the space probe).

Motion Diagram:

Motion Graphs: (Distinguish between the tracking device and the space station.)

A space probe travelling at v = 1.5 x 10³ i - 2.1 x 10² j + 4.5 x 10⁴ k m/s at r = 1.0 x 10¹¹ i + 6.1 x 10⁶ j + 4.5 x 10¹² k m (with respect to mission control) spots an enemy space station. The space station is travelling at v = 1.9 x 10³ i - 2.1 x 10² j + 4.5 x 10⁴ k m/s at r = 1.0 x 10¹¹ i + 6.7 x 10⁶ j + 4.5 x 10¹² k m (with respect to mission control). The space probe attempts to 'tag' the space station by attaching to it a tracking device. The space probe launches the tracking device at 500 m/s (with respect to the space probe).

Free Algebra tip: Use sin² u + cos² u =1 to eliminate u from the two equations.
Motion Information:
TRACKING DEVICE

Event 1 =		Event 2 =
t1 =		t2 =
x1 = y1 = z1 =		x2 = y2 = z2 =
vx1 = vy1 = vz1 =		vx2= vy2 = vz2 =

ax12 = ay12 = az12 =

SPACE STATION

Event 1 =		Event 2 =
t1 =		t2 =
x1 = y1 = z1 =		x2 = y2 = z2 =
vx1 = vy1 = v1z =		vx2= vy2 = vz2 =

	ax12 = ay12 = az12 =