Physics, 01.11.2020 09:20, mobslayer88

A golfer hits a shot to an elevated green. The ball leaves the club with an initial speed of 16 m/s at an angle of 58° above the hori-
zontal. If the speed of the ball just before it lands is 12 m/s, what is
the elevation of the green above the point where the ball is struck?

Answers: 1

Show answers

Answers

answered: moongirl4791

Approximately $5.7\; \rm m$ , assuming that the air resistance on this golf ball is negligible.

Explanation:

The mechanical energy of an object is the sum of its potential and kinetic energy.

If the air resistance on this golf ball is negligible, the mechanical energy of this golf ball should stay the same while it was in the air.

However, the final height of this ball is greater than its initial height. The ball has gained (gravitational) potential energy during the flight.

The mechanical energy of this ball has to stay the same during the flight. There was no energy input to the ball other than the initial push. Therefore, every joule of the potential energy that the ball has gained should correspond to one joule of kinetic energy that the ball loses.

The difference between the initial and final kinetic energy of this ball will thus be equal to the potential energy that the ball has gained. The elevation that the ball has gained may be found from the increase in the potential energy of this ball.

Steps

Let denote the mass of this golf ball.

Let v_0 and v_1 denote the initial and final (right-before-landing) speed of this ball, respectively. (The question states that $v_0 = 16\; \rm m \cdot s^{-1}$ while $v_0 = 12\; \rm m \cdot s^{-1}$ .)

Let denote the gravitational field strength. ( $g \approx 9.81\; \rm m\cdot s^{-1}$ .)

The initial kinetic energy of this golf ball would be:

$\displaystyle \text{Initial KE} = \frac{1}{2}\, m \cdot {v_0}^2$ .

The final (right-before-landing) kinetic energy of this golf ball would be:

$\displaystyle \text{Final KE} = \frac{1}{2}\, m \cdot {v_1}^2$ .

$\text{Initial KE} \text{Final KE}$ because v_0 < v_1 and m 0 .

Calculate the kinetic energy that this golf ball has lost during the flight:

$\begin{aligned}& \text{KE Lost} \\ &= \text{Initial KE} - \text{Final KE} \\ &= \frac{1}{2}\, m\cdot {v_0}^2 - \frac{1}{2}\, m\cdot {v_1}^2 = \frac{1}{2}\, m \,\left( {v_0}^2 - {v_1}^2\right)\end{aligned}$ .

Based on the assumptions, the kinetic energy that this golf ball has lost should be equal (in size) to the potential energy that this golf ball has gained:

$\begin{aligned} \text{PE Gained} = \text{KE Lost} &= \frac{1}{2}\, m \,\left( {v_0}^2 - {v_1}^2\right)\end{aligned}$ .

The potential energy that this golf ball has gained is proportional to the increase in its height. Let $\Delta h$ denote the elevation that this golf ball has gained.

$\text{PE Gained} = m \cdot g \cdot \Delta h$ .

Rearrange this equation and solve for $\Delta h$ :

$\begin{aligned}&\Delta h \\ &= \frac{\text{PE Gained}}{m \cdot g} \\ &= \frac{(1/2)\, m \,\left( {v_0}^2 - {v_1}^2\right)}{m \cdot g} = \frac{{v_0}^2 - {v_1}^2}{2\, g}\end{aligned}$ .

Given that $v_0 = 16\; \rm m \cdot s^{-1}$ , $v_1 = 12\; \rm m \cdot s^{-1}$ , and assume that $g \approx 9.81\; \rm m \cdot s^{-2}$ , calculate the elevation that this golf ball has gained:

$\begin{aligned}&\Delta h \\ &= \frac{{v_0}^2 - {v_1}^2}{2\, g} \\ &= \frac{\left(16\; \rm m \cdot s^{-1}\right) - \left(12\; \rm m \cdot s^{-1}\right)}{2\times 9.81\; \rm m \cdot s^{-2}} \approx 5.71\; \rm m\end{aligned}$ .

answered: Guest

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.

answered: Guest

Answertechnician (a) is correct;

Other questions on the subject: Physics

Physics, 22.06.2019 03:00, BeautyxQueen

Which of the following is not a part of the respiratory system? a. pharynx b. trachea c. pancreas d. larynx hurrim timed

Answers: 1

continue

Physics, 22.06.2019 14:10, momo842

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?

Answers: 1

continue

Physics, 22.06.2019 15:30, Mhayslett12

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin. answer in one word. part bfind e(r), the magnitude of the electric field at distance r from the point charge q. express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q. express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r

Answers: 2

continue

Physics, 22.06.2019 18:30, kennettahughley7964

Daughter element the new element produced along with a decay particle in a nuclear transmutation 2. half-life the substance that decays in a nuclear transmutation 3. parent element the change of one chemical element into another by nuclear decay or radioactive bombardment 4. transmutation the time required for the decay of one-half of the atoms in a sample of radioactive material

Answers: 2

continue

Do you know the correct answer?

A golfer hits a shot to an elevated green. The ball leaves the club with an initial speed of 16 m/s...