Projectile Motion Initial velocity is at an angle with respect to the horizontal. The only force on...

Projectile Motion

Initial velocity is at an angle with respect to the horizontal.

The only force on the projectile is the downward gravitational force of Earth on the projectile.

If you toss a ball horizontally in the +x direction, sketch the path of the projectile.

Example

Example

While standing on a 10-m high-dive, you throw a ball downward at an angle of 30 from the horizontal. Sketch the path of the ball.

x-component of motion

y-component of motion

A ball is rolled horizontally off a table. Assume air resistance is negligible. Then between the instant the ball leaves the table and the instant it strikes the floor, _________

A. vx = 0 and vy is constant but ≠ 0.

B. vx and vy are both constant but ≠ 0.

C. vx is constant but ≠ 0 and vy is increasing in magnitude.

D. vx is constant but ≠ 0 and vy is decreasing in magnitude.

E. vx and vy are both increasing in magnitude.

Velocity components vx and

vy

A ball is rolled horizontally off a table. Assume air resistance is negligible. Then between the instant the ball leaves the table and the instant it strikes the floor, _________

A. ax = 0 and ay is constant but ≠ 0.

B. ax and ay are both constant but ≠ 0.

C. ax is constant but ≠ 0 and ay is increasing in magnitude.

D. ax is constant but ≠ 0 and ay is decreasing in magnitude.

E. ax and ay are both increasing in magnitude.

Acceleration components ax

and ay

With negligible air resistance, the thrown ball follows the path traced in red. As it does so, the velocity of the shadow that it casts on the wall ________ and the velocity of the shadow that it casts on the ground __________.

A. becomes more positive and then less positive … doesn’t change

B. changes sign … doesn’t change

C. becomes more positive and then less positive … becomes more positive and then less positive

D. changes sign … becomes more positive and then less positive

E. doesn’t change … doesn’t change

Note: Each answer has a part for each blank.

With negligible air resistance, the thrown ball follows the path traced in red. In the coordinate frame shown, the ball’s acceleration is __________.

A. negative at points 1, 2, and 3

B. negative at point 1, zero at point 2, and positive at point 3

C. positive at point 1, zero at point 2, and negative at point 3

D. positive at points 1 and 3, but zero at point 2

E. negative at points 1 and 3, but zero at point 2

+

+x

1

2

3

A test rocket, due to technical failure, experiences no further thrust from the instant it leaves its ground level launching pad until it lands on the ground some distance away.

v0

a. During its flight, the rocket’s horizontal position x __________each time the clock advances by one second (t = 1 s).

changes by the same positive amount

changes by the same negative amount

remains unchanged

increases when the rocket is going up and decreases when it is coming back down

A.

B.

C.

D.


v0

b. During its flight, the rocket’s vertical position y __________each time the clock advances by one second (t = 1 s).



remains unchanged


A.

B.

C.

D.


v0

c. During its flight, the rocket’s horizontal velocity component vx

__________ each time the clock advances by one second (t = 1 s).



remains unchanged


A.

B.

C.

D.


v0

d. During its flight, the rocket’s vertical velocity component vy

__________ each time the clock advances by one second (t = 1 s).



remains unchanged


A.

B.

C.

D.


v0

e. At the highest point in it’s trajectory, the rocket’svelocity _____________ .A.

B.

C.

D.

is zero

is horizontal

is vertical

has both a horizontal and a vertical component

A. y and vy

B. x and vx

C. x and v

D. x and vy

E. ay and x

0 20 80 78.4 20-9.8 20 100 73.5 22.3-19.6 20 120 58.8 28-29.4 20 140 34.3 35.6-39.2 20 160 0 44

020406080100120140160180

0 5 10

t in seconds

x in meters

Series1

0102030405060708090

0 1 2 3 4 5 6 7 8

t in seconds

y in meters

Series1

0

10

20

30

40

0 4 8

t in seconds

vx in m/s

Series1

-50-40-30-20-1001020304050

0 4 8

t in seconds

vy in m/s

Series10102030405060708090

0 20 40 60 80 100

120

140

160

x in meters

y in meters

Series1

Series1

. .1 2

y

x

The graph above shows the path of a projectile that is unaffected by air resistance. The values of _______ are both different at point 1 than at point 2.

A. y and vy

B. x and vx

C. ay and v

D. ay and vy

E. ax and x

0 20 80 78.4 20-9.8 20 100 73.5 22.3-19.6 20 120 58.8 28-29.4 20 140 34.3 35.6-39.2 20 160 0 44

020406080100120140160180

0 5 10

t in seconds

x in meters

Series1

0102030405060708090

0 1 2 3 4 5 6 7 8

t in seconds

y in meters

Series1

0

10

20

30

40

0 4 8

t in seconds

vx in m/s

Series1

-50-40-30-20-1001020304050

0 4 8

t in seconds

vy in m/s

Series10102030405060708090

0 20 40 60 80 100

120

140

160

x in meters

y in meters

Series1

Series1

. .1 2

y

x

The graph above shows the path of a projectile that is unaffected by air resistance. The quantities _______ both have the same values at point 1 that they do at point 2.

Equations of Motion

Useful derived equations

Range


Peak height


time of flight

Example

A child swings on a playground swing and jumps off when the swing has a velocity of magnitude 5 m/s at an angle of 40 and she is 1 m off the ground. (a) What is her peak height and (b) where does she land?

Example

The world record shot put is 23.12 m by American Randy Barnes in 1990. If the shot left his hand at a height of 1.5 m and an angle of 45, what was the shot’s initial speed?

Projectile Motion Initial velocity is at an angle with respect to the horizontal. The only force on...

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