A car travels due east with a speed of 39.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 61.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (a) the car (b) the Earth Step 1 (a) To solve for the velocity of the rain relative to the car each moving relative to the Earth, we use the analogy of two objects moving relative to the Earth, each with constant velocity. Let VRC be the velocity of the rain relative to the car, V RE the velocity of the rain relative to the Earth, and VCE the velocity of the car relative to the Earth. Following the pattern of subscripts illustrated in the equation for two objects moving relative to the Earth, V AB with x- and y-components given by the following equations. v AE -V BE we find that the velocity of the rain relative to the car is VRC (VRC)X = (RE)x - (VCE)X (VRC)y= (RE)y - (VCE)y We choose a reference system with the positive x-axis in the eastward direction and the positive y-axis vertically upward. In this frame of reference, VCE = 39.0 km/h in the positive x-direction, and V = V in the negative y-direction. For the velocity components of the car and rain relative to the Earth, we have RE rain (VCE)X (VRE)X = 0, km/h), (CE)y = 0 (VRE) y = -Vrain Therefore, for the x-component of velocity of the rain relative to the car, we have (VRC)X = 0 - |km/h) = km/h), = VRE V == and for the y-component of velocity of the rain relative to the car, 0 = -Vrain (VRC) y = -Vrain CE'
A car travels due east with a speed of 39.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 61.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (a) the car (b) the Earth Step 1 (a) To solve for the velocity of the rain relative to the car each moving relative to the Earth, we use the analogy of two objects moving relative to the Earth, each with constant velocity. Let VRC be the velocity of the rain relative to the car, V RE the velocity of the rain relative to the Earth, and VCE the velocity of the car relative to the Earth. Following the pattern of subscripts illustrated in the equation for two objects moving relative to the Earth, V AB with x- and y-components given by the following equations. v AE -V BE we find that the velocity of the rain relative to the car is VRC (VRC)X = (RE)x - (VCE)X (VRC)y= (RE)y - (VCE)y We choose a reference system with the positive x-axis in the eastward direction and the positive y-axis vertically upward. In this frame of reference, VCE = 39.0 km/h in the positive x-direction, and V = V in the negative y-direction. For the velocity components of the car and rain relative to the Earth, we have RE rain (VCE)X (VRE)X = 0, km/h), (CE)y = 0 (VRE) y = -Vrain Therefore, for the x-component of velocity of the rain relative to the car, we have (VRC)X = 0 - |km/h) = km/h), = VRE V == and for the y-component of velocity of the rain relative to the car, 0 = -Vrain (VRC) y = -Vrain CE'
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11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![A car travels due east with a speed of 39.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on
the side windows of the car make an angle of 61.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.
(a) the car
(b) the Earth
Step 1
RC
RE
(a) To solve for the velocity of the rain relative to the car each moving relative to the Earth, we use the analogy of two objects moving relative to the
Earth, each with constant velocity. Let v be the velocity of the rain relative to the car, V the velocity of the rain relative to the Earth, and VCE the
velocity of the car relative to the Earth. Following the pattern of subscripts illustrated in the equation for two objects moving relative to the Earth, VAB =
V
VAE E-VBE we find that the velocity of the rain relative to the car is v
with x- and y-components given by the following equations.
CE
(VRC)X = (VRE)X - (VCE)X
RC) y = (VRE)y - (VCE)y
We choose a reference system with the positive x-axis in the eastward direction and the positive y-axis vertically upward. In this frame of reference, VCE
= 39.0 km/h in the positive x-direction, and V
in the negative y-direction. For the velocity components of the car and rain relative to the
RE
Earth, we have
(VCE)X =
(VRE)X = 0,
km/
= V
rain
(VCE) y = 0
RE)y = -Vrain
Therefore, for the x-component of velocity of the rain relative to the car, we have
(VRC)X = 0 -
| km/h) = -([
] km/h),
and for the y-component of velocity of the rain relative to the car,
(VRC)y=-Vrain - 0 = -Vrain](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84f39a0e-1c16-43ec-bcb3-7f889ca233a2%2Ff4d0f6bc-7294-4bed-a6d2-7d931d39e2f8%2Fq3qvhgr_processed.png&w=3840&q=75)
Transcribed Image Text:A car travels due east with a speed of 39.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on
the side windows of the car make an angle of 61.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.
(a) the car
(b) the Earth
Step 1
RC
RE
(a) To solve for the velocity of the rain relative to the car each moving relative to the Earth, we use the analogy of two objects moving relative to the
Earth, each with constant velocity. Let v be the velocity of the rain relative to the car, V the velocity of the rain relative to the Earth, and VCE the
velocity of the car relative to the Earth. Following the pattern of subscripts illustrated in the equation for two objects moving relative to the Earth, VAB =
V
VAE E-VBE we find that the velocity of the rain relative to the car is v
with x- and y-components given by the following equations.
CE
(VRC)X = (VRE)X - (VCE)X
RC) y = (VRE)y - (VCE)y
We choose a reference system with the positive x-axis in the eastward direction and the positive y-axis vertically upward. In this frame of reference, VCE
= 39.0 km/h in the positive x-direction, and V
in the negative y-direction. For the velocity components of the car and rain relative to the
RE
Earth, we have
(VCE)X =
(VRE)X = 0,
km/
= V
rain
(VCE) y = 0
RE)y = -Vrain
Therefore, for the x-component of velocity of the rain relative to the car, we have
(VRC)X = 0 -
| km/h) = -([
] km/h),
and for the y-component of velocity of the rain relative to the car,
(VRC)y=-Vrain - 0 = -Vrain
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