105 20103 mt1

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PROBLEM (1) (25 points) A A driver wants to jump across a 90-m wide canyon with his

B

y

car. The car starts from rest at point A, travels with a constant acceleration, moves horizontally off the cliff on the higher

g

side through point B into the air and lands on the edge of the

x

C

120 m

cliff at point C, on the lower side. Express your answers to

75 m

two significant figures. (g = 10 m/s2)

90 m

(a) (6 pts) Find the time it takes the car to go from B to C.

Let's take the origin at point B. 1 y f " y i = v yi t + a y t 2 where v yi = 0 2

2("45 m) "10 m/s 2 t = 3.0 s

2(y f " y i )

t= !

t=

!

ay !

a y = "g = "10 m/s 2 !y f " y i = "(120 m " 75 m) = "45 m

! ! (b) (6 pts) Find the speed at which the car moves off the cliff at B.

x f " x i = v xi t

v xi = !

x f " xi t

=

90 m 3.0 s

v xi = 30 m/s

! (c) (7 pts) Find!the car's velocity just before it lands at C. Express your answer in unit vectors.

" " ! v f = v xf i + v yf j " " " " ! v f = (30 i " 30 j) m/s = 30( i " j) m/s

v xf = v xi = 30 m/s

v yf = v yi + a y t = 0 + ("10 m/s 2 )(3.0 s) = "30 m/s !

!

!

! (d) (6 pts) Assuming the acceleration of the car from A to B was 5.0 m/s2, find the distance between A and B.

v xf2 = v xi2 + 2a x (x f " x i ) x f " xi =

!

v xf2

" v xi2

2a x

=

v xf2

"0

2a x

Notice: Alternative solution is possible. 2

=

(30 m/s) 2(5.0 m/s 2 )

x f " x i = 90 m

! !

Phys 105 First Midterm Examination

Page 1

Friday, 15-Jul, 2011


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