Here's how I would do it:
How far does he have to go to catch the bug ? <u>23.8 meters</u>
How soon does he want to get there ? <u>1.8 seconds</u>
What speed does he need ? (23.8 m) / (1.8 sec) = <u>13.222 m/sec</u>
What speed is he flying now? <u>3.7m/s</u>
How much does he need to increase it ? (13.222 - 3.7) = <em>9.5 m/s</em> faster
Answer:
(a) A = 0.700m
(b) k = 80.6N/m
(c) x = -0.699m
(d) x = -0.350m
(e) t = 0.168s
Explanation:
Given the equation of motion for the spring
X = 0.700cos(12.0t), m = 0.56kg
(a) A = amplitude = 0.700m
(b) The angular velocity ω = 12rad/s
ω = √(k/m)
ω² = k/m
k = m×ω² = 0.56×12² = 80.6N/m
Spring constant k = 80.6N/m
(c) T = 2π/ω = 2π/12
T = 0.524s
At t = T/2 = 0.524/2 = 0.262s
So x = 0.700cos(12×0.262) = –0.699m
(d) At t = 2/3×T = 2×0.524/3 = 0. 349s
x = 0.700cos(12×0.349) = –0.350m
(e) to find t at x = -0.300m
–0.300 = 0.700cos(12t)
–0.300/0.700 = cos(12t)
cos(12t) = –0.429
12t = cos-¹(-0.429)
12t = 2.01
t = 2.01/12
t = 0.168s
I will assume here that the well is sufficiently short so that the time the sound takes to come from the bottom of the well to our ear is negligible.
Since the pebble moves by uniformly accelerated motion, the distance it covers is given by
where
is the gravitational acceleration
is the time the pebble takes to reach the bottom of the well
Therefore, the depth of the well is
and the correct answer is B.
Answer: The answer is A) 49 N(Newtons).
Answer: Yes and no.
Explanation: Mass is the amount of matter in an object, whereas weight is the force exerted on an object by gravity. Objects on the surface of the earth have weight, although sometimes the weight is difficult to measure.
