0.18 m/s^2
Let's use the definition of energy and work to solve this problem. To make the math simple, I'll use a mass of 2 kg for the spacecraft.
Kinetic energy is expressed as E = 0.5 * M * V^2. So the energy of the spacecraft when initially observed is
E = 0.5 * M * V^2
E = 0.5 * 2 kg * (4 m/s)^2
E = 1 kg * 16 m^2/s^2
E = 16 kg*m^2/s^2
E = 16 J
Later the energy is
E = 0.5 * M * V^2
E = 0.5 * 2 kg * (9 m/s)^2
E = 1 kg * 81 m^2/s^2
E = 81 kg*m^2/s^2
E = 81 J
So while falling towards the asteroid, it gained (81 J - 16 J = 65 J) of energy over a distance of 180 meters. Since work is defined as force times distance, the force exerted upon that spacecraft is
65 J / 180 m
= 65 kg*m^2/s^2 / 180 m
= 0.361111111 kg*m/s^2
= 0.361111111 N
Dividing by the mass, gives
= 0.361111111 N / 2 kg
= 0.361111111 kg*m/s^2 / 2 kg
= 0.180555556 m/s^2
Now let's verify that answer. The equation for distance traveled with an initial velocity and under constant acceleration is
d = VT + 0.5AT^2
where
d = distance
V = initial velocity
T = time
A = acceleration
Let's substitute the known values and see what we get for T
d = VT + 0.5AT^2
180 = 4*T + 0.5*0.180555556*T^2
180 = 4*T + 0.090277778*T^2
0 = 4*T + 0.090277778*T^2 - 180
0.090277778*T^2 + 4*T - 180 = 0
Using the quadratic formula, I get T = -72, and T = 27.69230769.
Since we're not dealing with time travel, we'll use the positive value of
27.69230769 seconds.
The velocity after 27.69230769 seconds should be the initial velocity plus the time multiplied by the acceleration, so
4 m/s + 27.69230769 s * 0.180555556 m/s^2
= 4 m/s + 5 m/s
= 9 m/s
The velocity matches the acceleration, so the calculated acceleration of
0.180555556 m/s^2 is correct and when rounding to 2 significant figures is 0.18 m/s^2
Answer:
Explanation:
This is a displacement vector since it is defined in terms of distance (meters, to be exact). The way you find the y-component is
which says that you multiply the magnitude of the vector (its length) by the sin of the direction (the angle):
and get
12.1 m
Answer:
Frequency=10 Hz
Period=0.1 s
Explanation:
Frequency of a wave is the number of complete cycles per unit time. Usually, frequency is cycles per second, with unit as Heartz
Given cycles of the wave as 200 and time as 20 seconds
Frequency=200÷20=10 cycles per second
Therefore, frequency is 10 Hz
Period is usually the reviprocal of frequency hence reciprocal of 10 Hz will be 1/10=0.1 s
Answer:
Explanation:
The momentum of an object is given by .
Plugging in values, we have:
.