Answer:
The resultant vector is 1 m/s
Explanation:
The resultant vector is 1 m/s west based on triangle law of vector addition, when two sides of a triangle is represented by two vectors, the resultant vector is the third side of the triangle.
Answer:
The minumum speed the pail must have at its highest point if no water is to spill from it
= 2.64 m/s
Explanation:
Working with the forces acting on the water in the pail at any point.
The weight of water is always directed downwards.
The normal force exerted on the water by the pail is always directed towards the centre of the circle of the circular motion.
And the centripetal force, which keeps the system in its circular motion, is the net force as a result of those two previously mentioned force.
At the highest point of the motion, the top of the vertical circle, the weight and the normal force on the water are both directed downwards.
Net force = W + (normal force)
But the speed of this motion can be lowered enough to a point where the normal force becomes zero at the moment the pail reaches the highest point of its motion. Any speed lower than this value would result in the water spilling out of the pail. The water would not be able to resist the force of gravity.
At this point of minimum velocity,
Normal force = 0
Net force = W
Net force = centripetal force = (mv²/r)
W = mg
(mv²/r) = mg
r = 0.710 m
g = 9.8 m/s²
v² = gr = 9.8 × 0.71 = 6.958
v = √(6.958) = 2.64 m/s
Hope this Helps!!!
Answer:
The astronomical model created and published by Nicholas Copernicus in the year 1543 is called Copernican heliocentrism. The model set the Sun in immobile position near the center of the solar system with Earth, as well as the other planets, spherical, epicycled and at consistent frequencies around it.
Answer:
A) The space time coordinate x of the collision in Earth's reference frame is
.
B) The space time coordinate t of the collision in Earth's reference frame is

Explanation:
We are told a rocket travels in the x-direction at speed v=0,70 c (c=299792458 m/s is the exact value of the speed of light) with respect to the Earth. A collision between two comets is observed from the rocket and it is determined that the space time coordinates of the collision are (x',t') = (3.4 x 10¹⁰ m, 190 s).
An event indicates something that occurs at a given location in space and time, in this case the event is the collision between the two comets. We know the space time coordinates of the collision seen from the reference frame of the rocket and we want to find out the space time coordinates in Earth's reference frame.
<em>Lorentz transformation</em>
The Lorentz transformation relates things between two reference frames when one of them is moving with constant velocity with respect to the other. In this case the two reference frames are the Earth and the rocket that is moving with speed v=0,70 c in the x axis.
The Lorentz transformation is




prime coordinates are the ones from the rocket reference frame and unprimed variables are from the Earth's reference frame. Since we want position x and time t in the Earth's frame we need the inverse Lorentz transformation. This can be obtained by replacing v by -v and swapping primed an unprimed variables in the first set of equations




First we calculate the expression in the denominator


then we calculate t




finally we get that

then we calculate x






finally we get that

Answer:
120 miles per hour.
Explanation:
We need to find the time it takes my parents to drive home from the cottage. Since my father drives at 60 miles per hour, and the cottage is 240 miles from our home, and distance = speed × time. So, time = distance/speed = 240 mi/60 mi/h = 4 h.
So, it will take my father 4 hours to drive home from the cottage.
Since I have 2 hours to prepare for the party, the time left for me to drive to the cottage is 4 - 2 hrs = 2 hrs.
So, I'm supposed to drive to the cottage in at most 2 hours.
The speed at which I must drive in this time period is thus, speed = distance/time = 240 miles/2 hours = 120 miles per hour.
So, I must drive at a minimum speed of 120 miles per hour.