Firstly, let's convert the velocities in km/hr to m/s
32*1000/3600=8.89m/s
54*1000/3600=15m/s
From the formula, acceleration=V-U/t
15-8.89/8=0.76m/s²
hope this helps.
Answer:
spring compressed is 0.724 m
Explanation:
given data
mass = 1.80 kg
spring constant k = 2 × 10² N/m
initial height = 2.25 m
solution
we know from conservation of energy is
mg(h+x) = 0.5 × k × x² ...................1
here x is compression in spring
so put here value in equation 1 we get
1.8 × 9.8 × (2.25+x) = 0.5 × 2× 10² × x²
solve it we get
x = 0.724344
so spring compressed is 0.724 m
The displacement of the train after 2.23 seconds is 25.4 m.
<h3>
Resultant velocity of the train</h3>
The resultant velocity of the train is calculated as follows;
R² = vi² + vf² - 2vivf cos(θ)
where;
- θ is the angle between the velocity = (90 - 51) + 37 = 76⁰
R² = 8.81² + 9.66² - 2(8.81 x 9.66) cos(76)
R² = 129.75
R = √129.75
R = 11.39 m/s
<h3>Displacement of the train</h3>
Δx = vt
Δx = 11.39 m/s x 2.23 s
Δx = 25.4 m
Thus, the displacement of the train after 2.23 seconds is 25.4 m.
Learn more about displacement here: brainly.com/question/2109763
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Answer:
T = 1.2 s
T = 15.1 m = 15 m
Explanation:
This is a case of projectile motion:
TOTAL TIME OF FLIGHT:
The formula for total time of flight in projectile motion is:
T = 2 V₀ Sinθ/g
where,
T = Total Time of Flight = ?
V₀ = Launch Speed = 13.9 m/s
θ = Launch Angle = 25°
g = 9.8 m/s²
Therefore,
T = (2)(13.9 m/s)(Sin 25°)/(9.8 m/s²)
<u>T = 1.2 s</u>
<u></u>
RANGE OF BALL:
The formula for range in projectile motion is:
R = V₀² Sin2θ/g
where,
R = Horizontal Distance Covered by ball = ?
Therefore,
T = (13.9 m/s)²(Sin 2*25°)/(9.8 m/s²)
<u>T = 15.1 m = 15 m</u>
To solve this problem it is necessary to use the concepts related to Snell's law.
Snell's law establishes that reflection is subject to
![n_1sin\theta_1 = n_2sin\theta_2](https://tex.z-dn.net/?f=n_1sin%5Ctheta_1%20%3D%20n_2sin%5Ctheta_2)
Where,
Angle between the normal surface at the point of contact
n = Indices of refraction for corresponding media
The total internal reflection would then be given by
![n_1 sin\theta_1 = n_2sin\theta_2](https://tex.z-dn.net/?f=n_1%20sin%5Ctheta_1%20%3D%20n_2sin%5Ctheta_2)
![(1.54) sin\theta_1 = (1.33)sin(90)](https://tex.z-dn.net/?f=%281.54%29%20sin%5Ctheta_1%20%3D%20%281.33%29sin%2890%29)
![sin\theta_1 = \frac{1.33}{1.54}](https://tex.z-dn.net/?f=sin%5Ctheta_1%20%3D%20%5Cfrac%7B1.33%7D%7B1.54%7D)
![\theta = sin^{-1}(\frac{1.33}{1.54})](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20sin%5E%7B-1%7D%28%5Cfrac%7B1.33%7D%7B1.54%7D%29)
![\theta = 59.72\°](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2059.72%5C%C2%B0)
Therefore the
would be equal to
![\alpha = 90\°-\theta](https://tex.z-dn.net/?f=%5Calpha%20%3D%2090%5C%C2%B0-%5Ctheta)
![\alpha = 90-59.72](https://tex.z-dn.net/?f=%5Calpha%20%3D%2090-59.72)
![\alpha = 30.27\°](https://tex.z-dn.net/?f=%5Calpha%20%3D%2030.27%5C%C2%B0)
Therefore the largest value of the angle α is 30.27°