Answer:
a) 2/3 m/s
b) 0.0143 m/s
c) 0.00 m/s
Explanation:
a) 80 m / (2(60) s = 2/3 m/s
b) 2(80) / (3(3600) + (2 + 4)(60)) = 160 / 11,160 = 0.0143 m/s
c) start and end at your house. no displacement, no velocity.
Answer:
32.9166667 m / s^2
Explanation:
s = 4.25km (1000m / 1km)
= 4250m
u = 20m/s
delta T = 20min (60sec / 1min)
= 1200s
Use formula s = ut + (1/2)at^2
4250m = 20m/s * 1200s + (1/2)a*1200s^2
Rearrange it to find a
a = (s-ut) / (1/2 * t^2)
a = (4250m - 20m/s*1200s) / (1/2 * 1200s^2)
a = -32.9166667 m / s^2
Ek = 1/2mv^2
Ek = 1/2 * 30kg * 20^2 m/s
Ek = 6000J
Hope this Helps!
Answer:
![g_{moon}=1.67 [m/s^{2} ]](https://tex.z-dn.net/?f=g_%7Bmoon%7D%3D1.67%20%5Bm%2Fs%5E%7B2%7D%20%5D)
Explanation:
The weight of some mass is defined as the product of mass by gravitational acceleration. In this way using the following formula we can find the weight.

where:
w = weight [N]
m = mass = 0.06 [kg]
g = gravity acceleration = 10 [N/kg]
Therefore:
![w=0.06*10\\w=0.6[N]](https://tex.z-dn.net/?f=w%3D0.06%2A10%5C%5Cw%3D0.6%5BN%5D)
By Hooke's law we know that the force in a spring can be calculated by means of the following expression.

where:
k = spring constant [N/m]
x = deformed distance = 6 [cm] = 0.06 [m]
We can find the spring constant.
![k= F/x\\k=0.6/0.06\\k=10 [N/m]](https://tex.z-dn.net/?f=k%3D%20F%2Fx%5C%5Ck%3D0.6%2F0.06%5C%5Ck%3D10%20%5BN%2Fm%5D)
Since we use the same spring on the moon and the same mass, the constant of the spring does not change, the same goes for the mass.
![F_{moon}=k*0.01\\F = 10*0.01\\F=0.1[N]](https://tex.z-dn.net/?f=F_%7Bmoon%7D%3Dk%2A0.01%5C%5CF%20%3D%2010%2A0.01%5C%5CF%3D0.1%5BN%5D)
Since this force is equal to the weight, we can now determine the gravitational acceleration.
![F=m*g_{moon}\\g=F/m\\g = 0.1/0.06\\g_{moon} = 1.67[m/s^{2} ]](https://tex.z-dn.net/?f=F%3Dm%2Ag_%7Bmoon%7D%5C%5Cg%3DF%2Fm%5C%5Cg%20%3D%200.1%2F0.06%5C%5Cg_%7Bmoon%7D%20%3D%201.67%5Bm%2Fs%5E%7B2%7D%20%5D)
<span>To answer this question, the equation that we will be using is:
y = A cos bx + c
where A = amplitude, b = 2 pi/Period, Period = 12 hrs, c = midline,
x = t and y = f(t)
A = 1/2 (Xmax - Xmin)
12 - 2 / 2 = 10/2 = 5
b = 2 pi / 12 = pi/6
c = 1/2 (Xmax + Xmin)
12+2/2 = 7
answer: f(t) = 5 cos pi/6 t + 7 </span>