Answer:
0.68 s
Explanation:
We are given that
Initial velocity of box=
Final velocity of box=v=11.5 m/s
Distance=d=8.5 m
We have to find the time taken by box to slow by this amount.
We know that

Substitute the values




We know that
Acceleration=
Substitute the values



Hence, the time taken by box to slow by this amount=0.68 s
Answer:
The amplitude is
Explanation:
From the question we are told that
The frequency of when sound is approaching observer is 
The frequency as the move away from observer is 
The time between the pitch are 
Here you are the observer and your friends are the source of the sound
The period is mathematically evaluated as

as it is the time to complete one oscillation which from on highest pitch to the next highest pitch
Now T can also be mathematically represented as

Where
is the angular velocity
=> 
=> 
Now using Doppler Effect,
The source of the sound is approaching the observer
The


Where A is the amplitude
So when the source is moving away from the observer
Here
is the fundamental frequency
Dividing the both equation we have




=> 

Answer: Hence, the final temperature is 350 K
Explanation :
To calculate the final temperature of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.
Mathematically,

where,
are the initial pressure and temperature of the gas.
are the final pressure and temperature of the gas.
We are given:

Putting values in above equation, we get:

Hence, the final temperature is 350 K
Out of the choices given, igniting the gas-air mixture supplies the heat for the hot reservoir in a car's engine. The correct answer is C.
You are running at constant velocity in the x direction, and based on the 2D definition of projectile motion, Vx=Vxo. In other words, your velocity in the x direction is equal to the starting velocity in the x direction. Let's say the total distance in the x direction that you run to catch your own ball is D (assuming you have actual values for Vx and D). You can then use the range equation, D= (2VoxVoy)/g, to find the initial y velocity, Voy. g is gravitational acceleration, -9.8m/s^2. Now you know how far to run (D), where you will catch the ball (xo+D), and the initial x and y velocities you should be throwing the ball at, but to find the initial velocity vector itself (x and y are only the components), you use the pythagorean theorem to solve for the hypotenuse. Because you know all three sides of the triangle, you can also solve for the angle you should throw the ball at, as that is simply arctan(y/x).