Answer:
41.0 m/s, 10.6 s
Explanation:
Given:
a = -4.8 m/s²
Δy = 165 m
v = -10.0 m/s
Find: v₀ and t
v² = v₀² + 2aΔy
(-10.0 m/s)² = v₀² + 2(-4.8 m/s²) (165 m)
v₀ = 41.0 m/s
Δy = vt − ½ at²
165 m = (-10.0 m/s) t − ½ (-4.8 m/s²) t²
165 = -10t + 2.4t²
0 = 2.4t² − 10t − 165
Solve with quadratic formula:
t = [ -(-10) ± √((-10)² − 4(2.4)(-165)) ] / 2(2.4)
t = (10 ± √1684) / 4.8
t = 10.6 s
Answer
The refracted wave must obey Snell's equation
Ni sin θi = Nr sin θr
If Nr differs from Ni then sin θr will differ from sin θi
If the wave originates from point A and ends at point B then Snell's Law shows that the time for light to get from point A to point B is a minimum.
Average velocity is different than average speed because calculating average velocity involves considering the direction the bodies are moving.
When calculating average speeds you don't have to consider directions of the bodies.
This is because velocity is a vector quantity which must be defined by direction. Speed is a scalar quantity thus it does not have to be defined by direction.
Answers:
a)The balloon is 68 m away of the radar station
b) The direction of the balloon is towards the radar station
Explanation:
We can solve this problem with the Doppler shift equation:
(1)
Where:
is the actual frequency of the sound wave
is the "observed" frequency
is the velocity of sound
is the velocity of the observer, which is stationary
is the velocity of the source, which is the balloon
Isolating :
(2)
(3)
(4) This is the velocity of the balloon, note the negative sign indicates the direction of motion of the balloon: It is moving towards the radar station.
Now that we have the velocity of the balloon (hence its speed, the positive value) and the time (
) given as data, we can find the distance:
(5)
(6)
Finally:
(8) This is the distance of the balloon from the radar station
Yes. A roulette ball circulating in a spinning wheel, a car going around a curved
road at 30 mph, and a planet in a circular orbit are all being accelerated.
"Acceleration" does NOT mean "speeding up". It means any change in the
speed or DIRECTION of motion.
