asst 16 projectile motion ans

8/12/2019 Asst 16 Projectile Motion Ans

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Assignment 16 Projectile Motion Name

……………………………..

For all questions, assume air resistance is negligible. Use “g” = 1ms!"

1. Amelia throws a netball vertically. What happens to the #orce on theball as it rises, stops then falls?

Force due to gravity is constant (downwards) the whole time

. Amelia throws a netball vertically. What happens to the acceleration ofthe ball as it rises, stops then falls?

acceleration due to gravity force is constant (downwards) the whole time (yes

even at the highest point)

!. Amelia throws a netball vertically. What happens to the $elocit% of theball as it rises, stops then falls?

velocity starts ma"imum upwards, decreases to #ero (at highest point) thenincreases but downwards.

$. What is the si&e and 'irection of the acceleration as it rises and at the(ig(est )oint?

%.&ms' downwards%.&ms' downwards

. escribe what 1* ms' actually means.

An increase or decrease of velocity by 1*ms'1 in one second.

+. enny is roc- climbing. he drops a carabineer. /ow fast is it fallingafter (a) 1 s? (b) s?

(a) 1* ms'1

(b) * ms'1

0. ridget throws a netball hori#ontally at 1* ms'1

and drops another fromthe same height. 2"plain which lands first.

oth land at the same time because the both have the same verticalacceleration. (sideways motion doesn3t affect vertical motion)



&. ridget throws a netball hori#ontally at 1* ms'1

from a height of 1.& m.

(a)/ow long does it ta-e to land?

(b) /ow far does it go hori#ontally

(a) consider vertical motion.21

2

2121.8 0 9.8

0.60

id v t at

t

t s

= +

= + × ×

=

(b)consider hori#ontal motiond / 4 v " t d 4 1* " *.+* d 4 +.* m.

%. ridget throws the netball hori#ontally again from a height of 1.& m. 5t

lands $.* m away. /ow fast did she throw it?21

2

2121.8 0 9.8

0.60

id v t at

t

t s

= +

= + × ×

=

14.0

6.70.60

H H

H

d v

t

v ms−

=

= =

1*. What happens to the (ori&ontal component of the ball3s velocity asit falls?



/ori#ontal component of velocity always remains constant as there is nohori#ontal force6

11.What happens to the $ertical component of the ball3s velocity as itfalls?

7ertical component of velocity increases at 1* ms ' due to gravity force.

1. ridget then throws the netball upward at an angle. What happensto the vertical component of its velocity as it rises? As it falls?

8he vertical component of velocity decreases as the stone rises, is #ero as it changes direction9 the vertical velocity increases at 1* ms '1 each secondas it falls.

1!. What happens to the hori#ontal component of its velocity as itrises? As it falls?

remains constant

1!. A pro:ectile falls beneath the straight'line path it would follow ifthere were no gravity. /ow many meters does it fall below the line if ithas been travelling for 1s? For s?

d 4 ;at

where a 4 1*ms '

. After 1 s the distance is m. After s, distanceis *m.

1$. oes your answer to the last <uestion depend on the angle atwhich it was launched?

=>6 Acceleration remains the same.

1. A pro:ectile is launched vertically at 1** ms'1. 5f air resistance canbe neglected, at what velocity will it return to its initial level?

'1** ms '1 .

1+. uppose you roll a ball off a tabletop. Will the time to hit thefloor depend on the speed of the ball? 2"plain your answer.



=o. 7ertical motion is independent of hori#ontal motion. 8he distancecovered by the ball is given by d 4 ;at , so the time ta-en is independentof the initial hori#ontal velocity.

10. 5f you toss a ball vertically upward in a uniformly moving train,where will it land? 2"plain why.

5t will land in the same place on the train. 8he ball has the same sidewaysvelocity as the train. 5f it is thrown vertically, it will -eep the samesideways velocity as the train as it has no sideways force on it.

1&. A bomb accidentally falls from a high'flying airplane :ust as itflies directly above a shiny red orsche par-ed in a carpar-. elative tothe orsche, where will the bomb land?

8he bomb will land past the orsche. istance depends on height and speed of plane.

1%. 5n the absence of air drag, why does the vertical component ofvelocity for a pro:ectile change with time, whereas the hori#ontalcomponent of velocity doesn3t?

8here is a vertical force (i.e. gravity) but no hori#ontal force, thereforethere will be no change in the hori#ontal velocity (=ewton3s 1 st @aw)

*. A friend claims that bullets fired by some high'powered riflestravel for many meters in a straight line path before they start to fall.Another friend disputes this claim and states that all bullets from anyrifle drop below the straight line path a vertical distance given by

d 4 ;at

and that the curved path is obvious for low velocities and lessobvious for high velocities. =ow it3s your turn. Will all bullets drop thesame vertical distance in e<ual times? 2"plain.

5n the absence of other forces, any ob:ect falls at a rate of 1* ms ' due to gravity, so all ob:ects would fall the same distance below the straight linepath in a given time. /owever, a slow ob:ect will cover a shorter hori#ontaldistance in the same time, so it3s tra:ectory will be more curved than that ofa faster ob:ect.



1. An aeroplane is flying hori#ontally with a speed of 1*** -mh'1 (&*ms'1) when an engine falls off. =eglecting air resistance, assume it ta-es!* s for the engine to hit the ground.

(a) /ow high is the plane?

d 4 ;at 4 *. " 1* " !* 4 $ ** m

(b) /ow far (ori&ontall% does the engine travel while it falls?

d 4 v " t 4 &* " !* 4 & $** m

. 5f the aeroplane somehow continued to fly as if nothing hadhappened, where is the engine relative to the aeroplane at the moment

the engine hits the ground?irectly below (has the same hori#ontal velocity as the aeroplane).

!. organ and Anna loo- from their &* m high'rise balcony to aswimming pool below, * m out from the bottom of their building. 8heywonder how fast they would have to :ump hori#ontally to succeed inreaching the pool. What is the answer?

7ertical motionB t 4 C(dDg) 4 ( " &*D1*) 4 $ s

/ori#ontal motionB d 4 v " t 4E v 4 dDt 4 *D$ 4 ms '1

$. What is the ma"imum speed possible for a hori#ontally movingtennis ball as it clears the net 1.* m high and stri-es within the court3sborder, 1.* m distant?

7ertical motionB t 4 C(dDg) 4 ( " 1D1*) 4 C*. s

/ori#ontal motionB v 4 dDt 4 1D*.$ 4 0 ms '1

.



. raw labelled $elocit% and acceleration vectors on the ball inflight.

+. arah -ic-s a soccer ball at a speed of * ms'1

at !*o

to theground.a. alculate the hori#ontal component of velocity.

1

cos

cos3020

17

o x

x

adj

hyp

v

v ms

θ

−

=

=

=

b. alculate the initial vertical component of velocity.

1

sin

sin3020

10

yo

y

opp

hyp

v

v ms

θ

−

=

=

=

c. alculate the flight time.time ta-en is the same as if it was thrown straight up at 1*ms'1

find the time to get to highest point. ultiply by

a

a

a

v

v

v

30o

20ms-1V

y

Vx



0 10 ( 9.8 )

1.0

2.0

f iv v at

t

t s

total time s

= +

= + + − ×

=

=

d. alculate how high it goesto find height, use $ertical component of velocity

212

21210 1 9.8 1

5.1

id v t at

d

d m

= +

= × − × ×

=

e. alculate how far it goesto find distance use (ori&ontal component of velocity

17 2 35 H d v t m= = × =

0. halini -ic-s a soccer ball across the length of the school pool at aspeed of 1 ms'1 at $o to the ground. oes it reach the other end ordoes it fall in the water? Gustify your answer.



1 1

1

H

H

cos 45 sin 4515 15

10.6 10.6

time to highest oint....

0 10.6 9.8

1.06

2.12

!se ho"i#onta$ ve$ocity comonenet to %in& &istance

&& 10.6 2.

yo o x

x y

f i

H

vv

v ms v ms

use v v at

t

t ms

total time s

v t

− −

−

= =

= =

→ = +

= − ×

=

=

= ×

= ×

H

12

& 22 .

it %a$$s in the 'ate" (ass!ming oo$ is 25m)

m

NO

=

&. ose is on a tramping trip. /er friend is across a river and shewants to throw a cell phone to her. 8he river is !* m wide.

a. At what angle should she throw it?$o for ma"imum range

b. how that the minimum speed she can throw it is 10 ms'1

consider the motion to the highest point.

8he river is !* m so at the highest point it must have moved 1m hori#ontally

45o

15ms-1V

y

Vx



ho"i#onta$ ve"tica$

15 0 9.8

9.8comine aove e!ations

15 ( )9.8

%o" an a

f i

h h v v

h v

v

vh

d v t v v at

v t v t

vt

vv

= × = +

= × = − ×

=

=

0

h

2

2 2 2

1

ng$e o% 45 v

15 9.8

300

17

v

h

v h

v

v

v v v

v

v ms−

=

= ×

= +

=

=

HAIro:ectile motion• no hori#ontal force so hori#ontal velocity is constant

• vertical component is the same as for an ob:ect falling down vertically Jthe faster the ob:ect falls the greater the distance covered each second

• curved path followed by a pro:ectile is a combination of hori#ontal andvertical motion

ro:ectiles launched hori#ontally• hori#ontal velocity is constant so ball travels same hori#ontal distance each

second• ball accelerates downwards due to gravity so ball covers larger vertical

distance each second• tra:ectory is a parabola

45o

vV

y

Vx



ro:ectiles launched at an angle• pro:ectile drops a distance of t below the straight line path each second• hori#ontal component of velocity is constant so ball covers e<ual hori#ontal

distance each second• vertical component of velocity changes J decreases on way up9 #ero at

#enith9 increases on way down• complementary angles give same hori#ontal range• smaller angle 4E less time in the air 4E less range• ma"imum range for angle of $K

asst 16 projectile motion ans

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