Two lenses, with f 1 = +20.0 cm and f 2 = +30.0 cm, are placed on the x axis, as shown in Figure 27-28 An object is fixed 50 0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to lens 2 for the following cases: (a) x = 115 cm; (b) x = 30.0 cm; (c) x = 0 (d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, 1/ f eff = 1.
Two lenses, with f 1 = +20.0 cm and f 2 = +30.0 cm, are placed on the x axis, as shown in Figure 27-28 An object is fixed 50 0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to lens 2 for the following cases: (a) x = 115 cm; (b) x = 30.0 cm; (c) x = 0 (d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, 1/ f eff = 1.
Two lenses, with f1 = +20.0 cm and f2 = +30.0 cm, are placed on the x axis, as shown in Figure 27-28 An object is fixed 50 0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to lens 2 for the following cases: (a)x = 115 cm; (b)x = 30.0 cm; (c)x = 0 (d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, 1/feff = 1.
A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
2R
(b) the ball's speed at the peak of its path
v=
Rg 2
√ sin 26, V 3
(c) the initial vertical component of its velocity
Rg
sin ei
sin 20
(d) its initial speed
Rg
√ sin 20
×
(e) the angle 6, expressed in terms of arctan of a fraction.
1
(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.
hmax
R2
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
Xmax
R√3
2
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
A rocket is launched at an angle of 60.0° above the horizontal with an initial speed of 97 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 28.0 m/s². At this time, its engines fail and the rocket proceeds to move as a projectile.
(a) Find the maximum altitude reached by the rocket.
1445.46
Your response differs from the correct answer by more than 10%. Double check your calculations. m
(b) Find its total time of flight.
36.16
x
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. s
(c) Find its horizontal range.
1753.12
×
Your response differs from the correct answer by more than 10%. Double check your calculations. m
Chapter 27 Solutions
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