Which would require the greater change in the Earth's orbital speed (30 km/sec):
a) slowing it down so that it would crash into the Sun (0 km/sec), or
b) speeding it up so that it would escape from the Sun (42.5 km/sec)?
In order to crash into the sun, the Earth's orbital speed of 30 km/s would have to be
reduced to zero. This is a change of 30 km/s. In order to escape the Sun, the Earth's
orbital speed would have to be increased to 42.5 km/s, a change of 12.5 km/s. So a
greater change in speed is required to slow the Earth for a Sun crash than to speed it for
solar escape.
Which would require the greater change in energy?
a) slowing it down so that it would crash into the Sun, or
b) speeding it up so that it would escape from the Sun?
The energy needed to increase it from 30 km/s to 42.5 km/s is almost the same as the
energy needed to slow it to zero. That is,
ΔKE to escape from the Sun → ½m(42.5)2 - ½m(30)2 = 453m
ΔKE to hit the Sun → ½m(30)2 - ½m(0)2 = 450m
Recall that algebraically, (42.52- 302) does NOT equal (42.5 - 30)2!
Three baseballs are thrown from the top of the cliff
along paths A, B and C. If their initial speeds are the
same and there is no air resistance, the ball that strikes
the ground below with the greatest speed will follow path
The speed of impact for each ball is the same. With respect to the ground below, the
initial kinetic energy + potential energy of each ball is the same. This amount of energy
becomes the kinetic energy at impact. So for equal masses equal kinetic energies means
the same speed.
A rocket coasts in an elliptical orbit around the earth. To attain
escape velocity using the least amount of fuel in a brief firing time,
should it fire off at the apogee, or at the perigee?
The rocket will travel the greatest distance d during the brief firing time where it is
traveling fastest - at the perigee.
A rocket fired vertically at a speed of 11.2 km/s will
escape the earth. If it is instead launched horizontally
at the same speed, and it doesn't hit mountains or other
obstructions, and air resistance can be neglected, will
it still escape the earth?
Whether or not a body escapes the earth depends on whether or not it has sufficient
kinetic energy to equal the gravitational potential energy it would have infinitely far
away at 11.2 km/s, the rocket will have the same sufficient kinetic energy, whether it is
launched vertically or horizontally.
If two balls start simultaneously with the some initial speed, the ball to complete the
journey first is along
Although both balls have the same speed on the level parts of the tracks, the speeds
along the curved parts differ. The speed of the ball everywhere along curve B is greater
than the initial speed, whereas everywhere along curve A it is less. So the ball on track B
finishes first.
Consider the various positions of the satellite as it orbits the
planet as shown. with respect to the planet, in which position
does the satellite have the maximum
a) speed?
b) velocity?
c) momentum?
d) kinetic energy?
e) gravitational potential energy?
f) total energy
The satellite has greatest speed, velocity, momentum, and kinetic energy at the perigee,
position A.
It has greatest gravitational energy at the farthest position, the apogee at C.
Total energy, KE + PE, is the same at all positions.