We have the following equation for height:
h (t) = (1/2) * (a) * t ^ 2 + vo * t + h0
Where,
a: acceleration
vo: initial speed
h0: initial height.
The value of the acceleration is:
a = -g = -9.8 m / s ^ 2
For t = 0 we have:
h (0) = (1/2) * (a) * 0 ^ 2 + vo * 0 + h0
h (0) = h0
h0 = 0 (reference system equal to zero when the ball is hit).
For t = 5.8 we have:
h (5.8) = (1/2) * (- 9.8) * (5.8) ^ 2 + vo * (5.8) + 0
(1/2) * (- 9.8) * (5.8) ^ 2 + vo * (5.8) + 0 = 0
vo = (1/2) * (9.8) * (5.8)
vo = 28.42
Substituting values we have:
h (t) = (1/2) * (a) * t ^ 2 + vo * t + h0
h (t) = (1/2) * (- 9.8) * t ^ 2 + 28.42 * t + 0
Rewriting:
h (t) = -4.9 * t ^ 2 + 28.42 * t
The maximum height occurs when:
h '(t) = -9.8 * t + 28.42
-9.8 * t + 28.42 = 0
t = 28.42 / 9.8
t = 2.9 seconds.
Answer:
The ball was at maximum elevation when:
t = 2.9 seconds.
Answer & Explanation:
Scientists call them all electromagnetic radiation. The waves of energy are called electromagnetic (EM) because they have oscillating electric and magnetic fields. Scientists classify them by their frequency or wavelength, going from high to low frequency (short to long wavelength).
The mechanical energy of the girl will be conserved because the system is isolated and the initial potential energy will be equal to final kinetic energy.
<h3>
What is the law of conservation of energy?</h3>
The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another.
The change in the potential energy of the launched from a height into the pool without friction from the given height h is calculated by applying the following kinematic equation.
ΔP.E = ΔK.E
where;
- ΔP.E is change in potential energy of the child
- ΔK.E is change in the kinetic energy of the child
mghf - mghi = ¹/₂mv² - ¹/₂mu²
where;
- m is the mass of the girl
- g is acceleration due to gravity
- hi is the initial height of the girl
- hf is the final height when she is launched into the pool
- u is the initial velocity
- v is the final velocity of the girl
Thus, for every closed or isolated system such as this case, mechanical energy is always conserved because the initial potential energy of the girl will be converted into her final kinetic energy.
Learn more about conservation of mechanical energy here: brainly.com/question/332163
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