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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"} {}

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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.

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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"} {}

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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.

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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"} {}

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A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/s, and her takeoff point is 1.80 m above the pool. (a) How long are her feet in the air? (b) What is her highest point above the board? (c) What is her velocity when her feet hit the water?

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(a) Calculate the height of a cliff if it takes 2.35 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.00 m/s. (b) How long would it take to reach the ground if it is thrown straight down with the same speed?

Path of a rock being thrown off of cliff. The rock moves up from the cliff top, reaches a transition point, and then falls down to the ground.

(a) 8.26 m

(b) 0.717 s

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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?
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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
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Can you compute that for me. Ty
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what is inorganic
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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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
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progressive wave
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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?
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Who can show me the full solution in this problem?
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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