Physics

Monday, 16 April 2012

Gizmos: Golf Range Quiz

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Assessment Results » Golf Range

Individual Report: Asha Hashim

Student	1	2	3	4	5	Total
Hashim, Asha	B	C	B	A	D	(5/5)

The golf ball below has reached the top of its trajectory in the time shown. What will the total hang time be when the ball hits the ground? Assume no air resistance or spin.

A. 6.15 seconds
B. 8.20 seconds
C. 12.30 seconds
D. 16.40 seconds

Correct Answer: B — 8.20 seconds
Explanation: Assuming no spin, the flight of a golf ball is symmetrical; it takes the same amount of time to go up as it takes to come down. Since it took 4.10 seconds to rise to the top of it's trajectory, it will take another 4.10 seconds to descend, for a total hang time of 8.20 seconds.

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The golfer shown below has hit the ball with the initial velocity and launch angle shown. What was the initial horizontal velocity of the golf ball, v_x?

A. 29.0 m/s
B. 38.7 m/s
C. 41.0 m/s
D. 45.0 m/s

Correct Answer: C — 41.0 m/s
Explanation: To find the horizontal component of velocity, multiply the initial velocity by the cosine of the launch angle. The cosine of 45° is 0.7071, so the horizontal component of velocity is 58.0 • 0.7071 = 41.0 m/s.

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A cannon shoots a ball with an initial velocity of 152 m/s and a launch angle of 62°. The gravitational acceleration is 9.8 m/s². Assuming no air resistance, how long will the cannonball stay in the air?

A. 24.6 s
B. 27.4 s
C. 31.3 s
D. 39.7 s

Correct Answer: B — 27.4 s
Explanation: The hang time is independent of the horizontal velocity. To solve the problem, first calculate vertical velocity vector,

v_y = v_initial • sin(?)

Using this, the cannonball's initial vertical velocity is

v_y = 152 • sin(62) = 134.21 m/s

The next step is to calculate the hang time:

t = 2 • v_y / g

t = 2 • 134.2 / 9.8

t = 27.4 s

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On February 6, 1971, Alan Shepard made history by becoming the first astronaut to play golf on the Moon. Using only one hand to swing the club because of his bulky space suit, Shepard still managed a long drive. Given the lack of an atmosphere on the moon and a gravitational acceleration of 1.6 m/s², how far would the shot go with an initial velocity of 25 m/s and a launch angle of 35°?

A. 367 m
B. 375 m
C. 382 m
D. 391 m

Correct Answer: A — 367 m
Explanation: To solve the problem, first calculate the horizontal and vertical velocity vectors,

v_x = v_initial • cos(?)

v_y = v_initial • sin(?)

Using this, the initial velocity vectors are

v_x = 25 • cos(35) = 20.48 m/s

v_y = 25 • sin(35) = 14.34 m/s

The next step is to calculate the hang time:

t = 2 • v_y / g

t = 2 • 14.34 / 1.6

t = 17.92 s

Now, calculate the horizontal distance

d = v_x • t

d = 20.48 • 17.92 = 367.1 m

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On the famous 18th hole at Pebble Beach, Lionel Forrest stands next to his ball on the fairway, 165 meters from the hole. His caddie hands him a golf club that will hit the ball at a 65° angle. The gravitational acceleration is 9.8 m/s², and a stiff tailwind exactly cancels the effects of air resistance. How hard should Lionel hit the ball to land it as close to the hole as possible?

A. 43 m/s
B. 44 m/s
C. 45 m/s
D. 46 m/s

Correct Answer: D — 46 m/s
Explanation: Lionel will land his ball closest to the hole if he hits it with an initial velocity of 46 m/s. The simplest method of solving the problem is by trial and error. To solve the problem using algebra, start with the equation for the distance the ball will travel,

d = v_x • t

where t is the hang time of the ball. Also, we know that the hang time is twice the vertical velocity divided by gravitational acceleration,

t = 2 • v_y / g

By substitution,

d = 2 v_yv_x / g

Finally, we know that

v_x = v • cos(θ)

v_y = v • sin(θ)

So

d = 2v² cos(θ)sin(θ) / g

Solving for v²,

v² = gd / 2cos(θ)sin(θ)

Substituting the given values for distance, gravity, and launch angle,

v² = 9.8 • 165 / 2cos(65)sin(65)

v² = 2,110.8

v = 45.9 m/s

You answered this question correctly!

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Flying Machines

Before the Wright Brothers achieved the first successful controlled flight on December 17, 1903, hundreds of women and men attempted to fly, in airships, gliders and airplanes, and many could have become successful with a few minor adjustments.(1)Let us start off with the Wright brothers.

Wright Brothers - First Flight

(3)

The brothers built a movable track to help launch the Flyer. This downhill track would help the aircraft gain enough airspeed to fly. After two attempts to fly this machine, one of which resulted in a minor crash, Orville Wright took the Flyer for a 12-second, persistent flight on December 17, 1903. This was the first successful, powered, piloted flight in history. In 1904, the first flight lasting more than five minutes took place on November 9. The Flyer II was flown by Wilbur Wright. (2)

Leonardo Vinci

(1)

Leonardo was born in Vinci, Italy. He was first European interested in a sensible solution to flight. Leonardo designed a large amount of mechanical devices, including parachutes, and studied the flight of birds as well as their structure. About 1485 he drew detailed plans for a human-powered wing-flapping device planned to fly. There is no evidence that he actually attempted to build such a device, although the image he presented was a powerful one. (1)

Le Comte Ferdinand Charles Honore Phillipe d'Esterno

(1)

D'Esterno designed a flying machine to reproduce the various motions he thought were necessary for flight. Not surprisingly, his machine was quite bird-like; the outer and rear portions of the wings were to be flapped, while the front inner parts of the wings were fixed. The major horizontal tail surface was mounted on a general joint and the operator was able to move the machine's seat to change the center of gravity. While it seems clear that d'Esterno never attempted to build his machine. (1)

Joseph Michel Montgolfier

(4)

In 1782 in France, Joseph Michel Montgolfier filled a silk bag with hot air which, being less dense than the air around, it lifted the bag to the high ceiling of his house. On April 25, 1783, Joseph and his brother Jacques Etienne built a larger, circular bag, filled it with hot air from a fire and sent several farm animals in the air in a basket hung beneath it. After this success, they created an even larger envelope, and on November 21, 1783 in the Bois de Boulogne in Paris the brothers launched a 70-foot high balloon carrying Jean Francois Piltre de Rozier and the Marquis d’Artandes. (4)

As you can see many people in many different societies were able to think of an invention to help others to reach from point A to point B. Even though their plans were quite unique and largely different from one another, they all had the same goal in mind. They all wanted to produce a machine for man to fly.

Bibliography

1. PRESS, L. L., Ltd.., & Including.... (n.d.). The FLYING MACHINES Web Site. The FLYING MACHINES Web Site. Retrieved April 16, 2012, from http://www.flyingmachines.org/

2. Bellis, M. (n.d.). The Wright Brothers - First Flight of an Airplane. Inventors. Retrieved April 16, 2012, from http://inventors.about.com/od/wstartinventors/a/TheWrightBrother.htm

3. Houghton-mifflin, W. O. (n.d.). Wilbur and Orville Wright. Garden of Praise. [Print Photo]Retrieved from April 16, 2012, from http://www.gardenofpraise.com/ibdwrigh.htm

4. Yenne, B., & Morton. (n.d.). Hot Air Balloon History - Invention of the Hot Air Balloon. The Great Idea Finder - Celebrating the Spirit of Innovation . Retrieved April 16, 2012, from http://www.ideafinder.com/history/inventions/haballoon.htm

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