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2.6 Falling objects  (Page 6/9)

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An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration due to gravity have the same sign on the way up as on the way down?

Suppose you throw a rock nearly straight up at a coconut in a palm tree, and the rock misses on the way up but hits the coconut on the way down. Neglecting air resistance, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.

If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which it rises be affected?

The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?

How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of g size 12{g} {} on Earth)?

Problems&Exercises

Assume air resistance is negligible unless otherwise stated.

Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, and (d) 2.00 s for a ball thrown straight up with an initial velocity of 15.0 m/s. Take the point of release to be y 0 = 0 size 12{y rSub { size 8{0} } =0} {} .

(a) y 1 = 6 . 28 m size 12{y rSub { size 8{1} } =6 "." "28 m"} {} ; v 1 = 10 . 1 m/s size 12{v rSub { size 8{1} } ="10" "." "1 m/s"} {}

(b) y 2 = 10 . 1 m size 12{y rSub { size 8{2} } ="10" "." "1 m"} {} ; v 2 = 5 . 20 m/s size 12{v rSub { size 8{2} } =5 "." "20 m/s"} {}

(c) y 3 = 11 . 5 m ; v 3 = 0 .300 m/s size 12{v rSub { size 8{3} } =0 "." "300"" m/s"} {}

(d) y 4 = 10 .4 m ; v 4 = − 4 .60 m/s size 12{v rSub { size 8{4} } = - 4 "." "60"" m/s"} {}

Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, (d) 2.00, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.

A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player leave the ground to rise 1.25 m above the floor in an attempt to get the ball?

v 0 = 4 . 95 m/s size 12{v rSub { size 8{0} } =4 "." "95 m/s"} {}

A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40 m/s and observes that it takes 1.8 s to reach the water. (a) List the knowns in this problem. (b) How high above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.

A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable. (c) How long is the dolphin in the air? Neglect any effects due to his size or orientation.

(a) a = − 9 . 80 m/s 2 size 12{a= - 9 "." "80 m/s" rSup { size 8{2} } } {} ; v 0 = 13 . 0 m/s size 12{v rSub { size 8{0} } ="13" "." "0 m/s"} {} ; y 0 = 0 m size 12{y rSub { size 8{0} } ="0 m"} {}

(b) v = 0 m/s . Unknown is distance y to top of trajectory, where velocity is zero. Use equation v 2 = v 0 2 + 2 a y − y 0 size 12{v rSup { size 8{2} } =v rSub { size 8{0} } rSup { size 8{2} } +2a left (y - y rSub { size 8{0} } right )} {} because it contains all known values except for y , so we can solve for y size 12{y} {} . Solving for y size 12{y} {} gives

v 2 − v 0 2 = 2 a y − y 0 v 2 − v 0 2 2 a = y − y 0 y = y 0 + v 2 − v 0 2 2 a = 0 m + 0 m/s 2 − 13.0 m/s 2 2 − 9.80 m /s 2 = 8.62 m alignl { stack { size 12{v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } =2a left (y - y rSub { size 8{0} } right )} {} #{ {v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } } over {2a} } =y - y rSub { size 8{0} } {} # y=y rSub { size 8{0} } + { {v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } } over {2a} } =0`m+ { { left (0`"m/s" right ) rSup { size 8{2} } - left ("13" "." 0`"m/s" right ) rSup { size 8{2} } } over {2 left ( - 9 "." "80"`"m/s" rSup { size 8{2} } right )} } =8 "." "62"`m {}} } {}

Dolphins measure about 2 meters long and can jump several times their length out of the water, so this is a reasonable result.

(c) 2 . 65 s size 12{2 "." "65 s"} {}

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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what is viscosity?
David
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
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Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
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Source:  OpenStax, Cc test coll. OpenStax CNX. Dec 15, 2015 Download for free at http://legacy.cnx.org/content/col11717/1.4
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