Answer:
A dot B = C is the vector equation for this expression
A · B = A B cos θ
3 * 4 cos θ = 1 the value 1 is their dot product
cos θ = 1 / 12 = .083 θ = 85.2 deg
Answer:
Explanation:
Given
--- Ken's share
Required
The fraction each got
Since they both shared a cake, we have:
Substitute:
Factorize
Divide both sides by 3
Recall that:
Answer:
Explanation:
The centripetal acceleration of an object in circular motion is the acceleration with which the object is attracted towards the center of the circular orbit. Mathematically, it is given by
where
v is the speed of the object
r is the radius of the orbit
The speed of the object is also given by the ratio between the circumference of the orbit and the orbital period, T:
Substituting into the previous equation, we find a new expression for the centripetal acceleration:
In this problem:
- The radius of the orbit of the Moon is
- The period of the orbit is
Therefore, the centripetal acceleration is:
This problem is going to be pretty long to solve. So, prepare.
We’re interested in the change in our x position. So we have to break the velocity vector up into its components. Do cosine of 50 and then multiply by the magnitude of the velocity. I got 20.57m/s. That’s our initial velocity. And remember, horizontal acceleration is zero. The vertical acceleration, or any vertical component, has no effect on the horizontal components. In order to solve this problem, we want to utilize this equation:
Change in x-position = Vix*t
Let’s solve for time, which is dependent on the vertical components. The projectile will stop when it vertically hits the ground. Generally you want to use this equation for solving for time:
Yf = Yi + Viy*t + 1/2at^2
We didn’t solve for the vertical component yet, so let’s do that now. (Sine of 50)*(32) = 24.51m/s
Let’s now plug everything in:
0 = 0 + 24.5t - 4.9t^2
0 = 24.5t - 4.9t^2
0 = t(24.5 - 4.9t)
-24.5 = -4.9t
t = 5 seconds
The hard stuff is pretty much over. Put that 5 seconds into the other equation I said we wanted to use to solve the problem
Change in x-position (range) = (20.57)*(5)
= 102.85 meters
Answer B
Answer:
υ = 345.82 m/s
Explanation:
The formula used to find the speed of sound in air, at different temperatures is given as follows:
where,
υ = speed of sound at given temperature = ?
υ₀ = speed of sound at 0°C = 331 m/s
T = temperature in K = 15°C + 273 = 298 k
Therefore, using these values in the equation, we get:
<u>υ = 345.82 m/s</u>
