This preview shows page 1. Sign up to view the full content.
Unformatted text preview: m ) 2
5
2
= 4.90 × 10 m s . (b) The average velocity as the front of the bullet passes through the board is
v f + vi
v board =
= 350 m s and the total time of contact with the board is
2 t= ( ∆x )board Lbullet
v board + vf = 0.100 m 0.0200 m
+
= 3.57 × 10−4 s
350 m s 280 m s (c) From v 2 = v i2 + 2 a( ∆x ) , with v f = 0 , gives the required thickness as
f ∆x = v 2 − v i2
f
2a = ( 0 − ( 420 m s ) 2 2 −4.90 × 105 m s 2 ) = 0.180 m . 41 CHAPTER 2.57 2 The falling ball moves a distance of (15 m − h) before they meet, where h is the height 1
above the ground where they meet. Apply ∆y = v i t + at 2 , with a = − g to obtain
2
1
1
− (15 m − h) = 0 − gt 2 , or h = 15 m − gt 2 .
2
2
1
1
Applying ∆y = v i t + at 2 to the rising ball gives h = ( 25 m s ) t − gt 2 .
2
2
Combining equations (1) and (2) gives t = 2.58 (1) (2) 15 m
= 0.60 s .
25 m s The distance required to stop the car after the brakes are applied is
2 ( ∆x ) stop ⎡
mi ⎛ 1.47 ft s ⎞ ⎤
0 − ⎢ 35.0
⎥
2
2
h ⎜ 1 mi h ⎟ ⎦
v f − vi
⎝
⎠
⎣
=
=
= 147 ft .
2a
2 −9.00 ft s 2 ( ) Thus, if the deer is not to be hit, the maximum distance the car can travel before the
brakes are applied is given by ( ∆x )before = 200 ft − ( ∆x ) stop = 200 ft − 147 ft = 53.0 ft .
Before the brakes are applied, the constant speed of the car is 35.0 mi/h. Thus, the time
required for it to travel 53.0 ft, and hence the maximum allowed reaction time, is ( tr )max = ( ∆x )before
vi = 53.0 ft
⎡
mi ⎛ 1.47 ft s ⎞ ⎤
⎢35.0
⎥
h ⎜ 1 mi h ⎟ ⎦
⎝
⎠
⎣ 42 = 1.03 s . CHAPTER 2.59 2 (a) When either ball reaches the ground, its net displacement is ∆y = −19.6 m . 1
Applying ∆y = v i t + at 2 to the motion of the first ball gives
2
1
2
−19.6 m = ( −14.7 m s ) t1 + −9.80 m s 2 t1 which has a positive solution of
2
t1 = 1.00 s . ( ) Similarly, applying this relation to the motion of the second ball gives
1
2
−19.6 m = ( +14.7 m s ) t 2 + −9.80 m s 2 t 2 which has a single positive solution of...
View
Full
Document
This note was uploaded on 03/03/2010 for the course PHY P221 taught by Professor Dr.ha during the Spring '05 term at Indiana University South Bend.
 Spring '05
 Dr.Ha
 Physics, Acceleration

Click to edit the document details