Answer:
6.0 s
98 m/s
Explanation:
The radius of the planet is much bigger than the height of the tower, so we will assume the acceleration is constant. Neglect air resistance.
Acceleration due to gravity on this planet is:
a = GM / r²
a = (6.67×10⁻¹¹ m³/kg/s²) (2.7 × 1.48×10²³ kg) / (1.7 × 750,000 m)²
a = 16.4 m/s²
The height of the tower is:
Δy = 96 × 3.05 m
Δy = 293 m
Given v₀ = 0 m/s, find t and v.
Δy = v₀ t + ½ at²
(293 m) = (0 m/s) t + ½ (16.4 m/s²) t²
t = 6.0 s
v² = v₀² + 2aΔy
v² = (0 m/s)² + 2 (16.4 m/s²) (293 m)
v = 98 m/s
Answer:
0.14 seconds
Explanation:
The speed of light in vacuum is approximately 3.0*10^8. The distance that would be covered by the object would be equivalent to the circumference of the cross-section of the earth on the equator.
Circumference = 2
*6400000 =4.02*10^7
Time = distance/speed = 4.2*10^7 / 3.0*10^8 =0.14s
Answer:
The minimum speed when she leave the ground is 6.10 m/s.
Explanation:
Given that,
Horizontal velocity = 1.4 m/s
Height = 1.8 m
We need to calculate the minimum speed must she leave the ground
Using conservation of energy



Put the value into the formula




Hence, The minimum speed when she leave the ground is 6.10 m/s.
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
