Answer:
b. v = 0, a = 9.8 m/s² down.
Explanation:
Hi there!
The acceleration of gravity is always directed to the ground (down) and, near the surface of the earth, has a constant value of 9.8 m/s². Since the answer "b" is the only option with an acceleration of 9.8 m/s² directed downwards, that would solve the exercise. But why is the velocity zero at the highest point?
Let´s take a look at the height function:
h(t) = h0 + v0 · t + 1/2 g · t²
Where
h0 = initial height
v0 = initial velocity
t = time
g = acceleration due to gravity
Notice that the function is a negative parabola if we consider downward as negative (in that case "g" would be negative). Then, the function has a maximum (the highest point) at the vertex of the parabola. At the maximum point, the slope of the tangent line to the function is zero, because the tangent line is horizontal at a maximum point. The slope of the tangent line to the function is the rate of change of height with respect to time, i.e, the velocity. Then, the velocity is zero at the maximum height.
Another way to see it (without calculus):
When the ball is going up, the velocity vector points up and the velocity is positive. After reaching the maximum height, the velocity vector points down and is negative (the ball starts to fall). At the maximum height, the velocity vector changed its direction from positive to negative, then at that point, the velocity vector has to be zero.
Answer:
The maximum pressure that will be attained in the tank before the plug melts and releases gas should be less than 74.26 atm.
Explanation:
To calculate the final pressure 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:
The maximum pressure that will be attained in the tank before the plug melts and releases gas should be less than 74.26 atm.
The given mass is 0.025563 g.
Examine the given choices.
a. 0.026 g
This uses 2 significant digits, with rounding to the 3rd decimal place.
b. 2.5 x 10² g = 250 g.
It is incorrect.
c. 0.025 g.
This uses 2 significant digits. It is inaccurate because it does not use rounding to the 3rd decimal place.
d. 0.02 g
This uses one significant digit. It is incorrect for representing the given data.
Answer: a. 0.026 g
Explanation:
Hydraulic systems use the pump to push hydraulic fluid through the system to create fluid power. The fluid passes through the valves and flows to the cylinder where the hydraulic energy converts back into mechanical energy. The valves help to direct the flow of the liquid and relieve pressure when needed
Answer:
2856.96 J
0
0
6.78822 m/s
Explanation:
= Initial velocity = 9.6 m/s
g = Acceleration due to gravity = 9.81 m/s²
h = Height
The athlete only interacts with the gravitational potential energy. Air resistance is neglected.
At height y = 0
Kinetic energy
At height y = 0 the potential energy is 0 as
At maximum height her velocity becomes 0 so the kinetic energy becomes zero.
As the the potential and kinetic energy are conserved
The general equation
Half of maximum height
The velocity of the athlete at half the maximum height is 6.78822 m/s