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Molodets [167]
2 years ago
9

1.An elevator is ascending with constant speed of 10 m/s. A boy in the elevator throws a ball upward at 20 m/ a from a height of

2 m above the elevator floor when the elevator floor when the elevator is 28 m above the ground.
a. What's the maximum height?
b. How long does it take for the ball to return to the elevator floor?​
Physics
1 answer:
laiz [17]2 years ago
6 0

(a) The maximum height reached by the ball from the ground level is 75.87m

(b) The time taken for the ball to return to the elevator floor is 2.21 s

<u>The given parameters include:</u>

  • constant velocity of the elevator, u₁ = 10 m/s
  • initial velocity of the ball, u₂ = 20 m/s
  • height of the boy above the elevator floor, h₁ = 2 m
  • height of the elevator above the ground, h₂ = 28 m

To calculate:

(a) the maximum height of the projectile

total initial velocity of the projectile = 10 m/s + 20 m/s  = 30 m/s (since the elevator is ascending at a constant speed)

at maximum height the final velocity of the projectile (ball), v = 0

Apply the following kinematic equation to determine the maximum height of the projectile.

v^2 = u^2 + 2(-g)h_3\\\\where;\\\\g \ is \ the \ acceleration \ due \ to\  gravity = 9.81 \ m/s^2\\\\h_3 \ is \ maximum \ height \ reached \ by \ the \ ball \ from \ the \ point \ of \ projection\\\\0 = u^2 -2gh_3\\\\2gh_3 = u^2 \\\\h_3 = \frac{u^2}{2g} \\\\h_3 = \frac{(30)^2}{2\times 9.81} \\\\h_3 = 45.87 \ m

The maximum height reached by the ball from the ground level (h) = height of the elevator from the ground level + height of he boy above the elevator + maximum height reached by elevator from the point of projection

h = h₁ + h₂ + h₃

h = 28 m + 2 m  +  45.87 m

h = 75.87 m

(b) The time taken for the ball to return to the elevator floor

Final height of the ball above the elevator floor = 2 m + 45.87 m = 47.87 m

Apply the following kinematic equation to determine the time to return to the elevator floor.

h = vt + \frac{1}{2} gt^2\\\\where;\\\\v \ is \ the \ initial \ velocity \ of \ the \ ball \ at \ the \ maximum \ height = 0\\\\h = \frac{1}{2} gt^2\\\\gt^2 = 2h\\\\t^2 = \frac{2h}{g} \\\\t = \sqrt{\frac{2h}{g}} \\\\t = \sqrt{\frac{2\times 47.87}{9.81}} \\\\t = 2.21 \ s

To learn more about projectile calculations please visit: brainly.com/question/14083704

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Answer:

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3 0
2 years ago
The spring is compressed a total of 3.0 cm, and used to set a 500 gram cart into motion. Find the speed of the cart at the insta
BartSMP [9]

Answer:

1.15 m/s

Explanation:

Part of the question is missing. Found the missing part on google:

"1. A hanging mass of 1500 grams compresses a spring 2.0 cm.   Find the spring constant in N/m."

Solution:

First of all, we need to find the spring constant. We can use Hooke's law:

F=kx

where

F=mg=(1.5 kg)(9.8 m/s^2)=14.7 N is the force applied to the spring (the weight of the hanging mass)

x = 2.0 cm = 0.02 m is the compression of the spring

Solving for k, we find the spring constant:

k=\frac{F}{x}=\frac{14.7}{0.02}=735 N/m

In the second part of the problem, the spring is compressed by

x = 3.0 cm = 0.03 m

So the elastic potential energy of the spring is

U=\frac{1}{2}kx^2=\frac{1}{2}(735)(0.03)^2=0.33 J

This energy is entirely converted into kinetic energy of the cart, which is:

U=K=\frac{1}{2}mv^2

where

m = 500 g = 0.5 kg is the mass of the cart

v is its speed

Solving for v,

v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(0.33)}{0.5}}=1.15 m/s

4 0
3 years ago
Air conditioners sold in the United States are given a seasonal energy-efficiency ratio (SEER) rating that consumers can use to
amid [387]

Answer:

112.58

Explanation:

The Coefficient of Performance of any system is denoted by COP=Q/W, where Q is the useful heat supplied or removed and W is the work required by the system. According to the first law of thermoddynamics Qh= Qc + W, where Qh is the heat transfered to the hot reservoir and Qc is the heat collected from the cold reservoir. Substituting the values for W and apllying the limitation for maximum theoretical efficiency we end up with the eqution shown below.

The Coefficient of Performance of air conditioner or COP is denoted by

COP(cool) = Tc/(Th- Tc)

where Tc: the lowest temperature

           Th: the highest temperature

converting the values to Kelvin and adding them in the above equation

COP(cool) = (25+273)/((34+273)-(25+273))

                 = 298/(307-298)

                 = 298/9 = 33.11

From the question, it is stated that COP=SEER/3.4

hence, SEER= COP * 3.4

SEER= 33.11 * 3.4 = 112.58

7 0
3 years ago
The index of refraction for a certain type of glass is 1.641 for blue light and 1.603 for red light. When a beam of white light
exis [7]

Answer:

The angle between the emergent blue and red light is 0.566^{o}

Explanation:

We have according to Snell's law

n_{1}sin(\theta _{i})=n_{2}sin(\theta _{r})

Since medium from which light enter's is air thus n_{1}=1

Thus for blue incident light we have

1\times sin(40.05)=1.641\times sin(\theta _{rb})\\\\\therefore \theta _{rb}=sin^{-1}(\frac{sin(40.05)}{1.64})\\\\\theta _{rb}=23.10

Similarly using the same procedure for red light we have

1\times sin(40.05)=1.603\times sin(\theta _{rr})\\\\\therefore \theta _{rr}=sin^{-1}(\frac{sin(40.05)}{1.603})\\\\\theta _{rr}=23.66^{o}

Thus the absolute value of angle between the refracted blue and red light is

|23.66-23.10|=0.566^{o}

6 0
3 years ago
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