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m_a_m_a [10]
3 years ago
15

The Hawaiian hot spot sits below the Pacific plate. As the plate moves over the hot spot, a chain of volcanoes is formed. The Ea

st Molokai Volcano is ~1.76 million years old, and about 178 km away from the current location of the Hawaiian hot spot. Assuming that the hot spot is in a fixed location, how fast (at what rate) is the Pacific plate moving?
Physics
1 answer:
Viktor [21]3 years ago
6 0

Answer:

3.2048179721\times 10^{-9}\ m/s

Explanation:

Assuming that the pacific plate moved 178 km in 1.76 million years.

s = Distance = 178 km

t = Time taken = 1.76 million years

Speed is given by

v=\dfrac{s}{t}\\\Rightarrow v=\dfrac{178000}{1.76\times 10^6\times 365.25\times 24\times 3600}\\\Rightarrow v=3.2048179721\times 10^{-9}\ m/s

The speed of the plate is 3.2048179721\times 10^{-9}\ m/s

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4 years ago
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A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle
xz_007 [3.2K]

Answer:

a) \Delta{t} = 5.39s

b) the motorcycle travels 155 m

Explanation:

Let t_2-t_1 = \Delta{t}, then consider the equation of motion for the motorcycle (accelerated) and for the car (non accelerated):

v_{m2}=v_0+a\Delta{t}\\x+d=(\frac{v_0+v_{m2}}{2} )\Delta{t}\\v_c = v_0 = \frac{x}{\Delta{t}}

where:

v_{m2} is the speed of the motorcycle at time 2

v_{c} is the velocity of the car (constant)

v_{0} is the velocity of the car and the motorcycle at time 1

d is the distance between the car and the motorcycle at time 1

x is the distance traveled by the car between time 1 and time 2

Solving the system of equations:

\left[\begin{array}{cc}car&motorcycle\\x=v_0\Delta{t}&x+d=(\frac{v_0+v_{m2}}{2}}) \Delta{t}\end{array}\right]

v_0\Delta{t}=\frac{v_0+v_{m2}}{2}\Delta{t}-d \\\frac{v_0+v_{m2}}{2}\Delta{t}-v_0\Delta{t}=d\\(v_0+v_{m2})\Delta{t}-2v_0\Delta{t}=2d\\(v_0+v_0+a\Delta{t})\Delta{t}-2v_0\Delta{t}=2d\\(2v_0+a\Delta{t})\Delta{t}-2v_0\Delta{t}=2d\\a\Delta{t}^2=2d\\\Delta{t}=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2*58}{4}}=\sqrt{29}=5.385s

For the second part, we need to calculate x+d, so you can use the equation of the car to calculate x:

x = v_0\Delta{t}= 18\sqrt{29}=96.933m\\then:\\x+d = 154.933

3 0
3 years ago
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vesna_86 [32]

Answer:

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3 years ago
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