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:
(a) 185 N/m
(b) 3.083 kg
Explanation:
(a)
Using,
E = 1/2ke²....................... Equation 1
Where E = work done to compress the spring, k = spring constant of the spring, e = compression of the spring.
make k the subject of the equation
k = 2E/e²............... Equation 2
Given: E = 3.7 J, e = 0.20 m
Substitute into equation 2
k = 2(3.7)/0.2²
k = 185 N/m.
(b)
Using,
F = ma.............. Equation 2
Where F = force applied to the spring, m = mass attached to the spring, a = acceleration of the spring.
But from hook's law,
F = ke................. Equation 3
substitute equation 3 into equation 2
ke = ma
make m the subject of the equation
m = ke/a................ Equation 4
Given: k = 185 N/m, e = 0.2 m, a = 12 m/s²
Substitute into equation 4
m = 185(0.2)/12
m = 3.083 kg
The nervous system is responsible for sending, receiving, and interpreting information from all parts of the body. The nervous system monitors and coordinates internal organ function and responds to changes in the external environment. (The role) The central nervous system consists of the brain and the spinal cord. It is part of the overall nervous system that also includes a complex network of neurons, known as the peripheral nervous system. (Central nervous system)
1. Always be the bigger person
2. Violence is never the answer
3. Don’t fight fire with fire
