Why does hitting a magnet with a hammer cause the magnetism to be reduced?
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Answer:
The ball lands 154.3 ft from the origin at an angle of 13.6° from the eastern direction toward the south.
Explanation:
Hi there!
The position vector of the ball is described by the following equation:
r = (x0 + v0x · t + 1/2 · ax · t², y0 + v0y · t + 1/2 · ay · t², z0 + v0z · t + 1/2 · g · t²)
Where:
r = poisition vector of the ball at time t.
x0 = initial horizontal position.
v0x = initial horizontal velocity (eastward).
t = time.
ax = horizontal acceleration (eastward).
y0 = initial horizontal position.
v0y = initial horizontal velocity (southward).
ay = horizontal acceleration (southward)
z0 = initial vertical position.
v0z = initial vertical velocity.
g = acceleration due to gravity.
We have to find at which time the vertical component of the position vector is zero (the ball is on the ground) and then we can calculate the horizontal distance traveled by the ball at that time, using the equations of the horizontal components of the position vector.
Let´s place the origin of the system of reference at the throwing point so that x0 and y0 and z0 = 0.
y = z0 + v0z · t + 1/2 · g · t² (z0 = 0)
0 = 48 ft/s · t - 1/2 · 32 ft/s² · t²
0 = t (48 ft/s - 16 ft / s² · t) (t= 0, the origin point)
0 = 48 ft/s - 16 ft / s² · t
- 48 ft/s / -16 f/s² = t
t = 3.0 s
Now, we can calculate how much distance the ball traveled in that time.
First, let´s calculate the distance traveled in the eastward direction:
x = x0 + v0x · t + 1/2 · ax · t² (x0 = 0, ax = 0 there is no eastward acceleration)
x = 50 ft/s · 3 s
x = 150 ft
And now let´s calculate the distance traveled in southward direction:
y = y0 + v0y · t + 1/2 · ay · t² (y0 = 0 and v0y = 0, initially, the ball does not have a southward velocity).
y = 1/2 · ay · t²
y = 1/2 · (-8 ft/s²) · (3 s)²
y = -36 ft
Then, the final position vector will be:
r = (150 ft, -36 ft, 0)
The traveled distance is the magnitude of the position vector:
To calculate the angle, we have to use trigonometry (see attached figure):
cos angle = adjacent side / hypotenuse
cos α = x/r
cos α = 150 ft / 154.3 ft
α = 13.6°
The ball lands 154.3 ft from the origin at an angle of 13.5° from the eastern direction toward the south.
Answer:
285.7s
Explanation:
Given parameters:
Speed of the person = 1.4m/s
Unknown:
Time it takes to walk one time round the track = ?
Solution:
The circumference of the track is 400m for a standard pitch.
Now;
Speed =
Time =
Now insert the parameters;
Time = = 285.7s
The beat frequency produced by the two standing waves is 13 Hz.
<h3>The wavelength of the shorter string</h3>The wavelength of the shorter string is calculated as follows;
The frequency of the longer string is calculated as follows;
The beat frequency produced by the two standing waves is calculated as follows;
Learn more about beat frequency here: brainly.com/question/3086912