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