1. Home
  2. Kinematics
  3. Kinematics
  4. 1.11 falling objects

0.10 1.11 falling objects  (Page 6/8)

<< Chapter < Page
  Kinematics     Page 6 / 8
Chapter >> Page >

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"} {}

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"} {}

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?

(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

You throw a ball straight up with an initial velocity of 15.0 m/s. It passes a tree branch on the way up at a height of 7.00 m. How much additional time will pass before the ball passes the tree branch on the way back down?

1.91 s

A kangaroo can jump over an object 2.50 m high. (a) Calculate its vertical speed when it leaves the ground. (b) How long is it in the air?

Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a hiker hears a rock break loose from a height of 105 m. He can’t see the rock right away but then does, 1.50 s later. (a) How far above the hiker is the rock when he can see it? (b) How much time does he have to move before the rock hits his head?

(a) 94.0 m

(b) 3.13 s

Suppose you drop a rock into a dark well and, using precision equipment, you measure the time for the sound of a splash to return. (a) Neglecting the time required for sound to travel up the well, calculate the distance to the water if the sound returns in 2.0000 s. (b) Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 332.00 m/s in this well.

(a) 19 . 6 m size 12{"19" "." "6 m"} {}

(b) 18 . 5 m size 12{"18" "." "5 m"} {}

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

(a) 305 m

(b) 262 m, -29.2 m/s

(c) 8.91 s

A soft tennis ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.10 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms ( 3 . 50 × 10 − 3 s ) size 12{ \( 3 "." "50" times "10" rSup { size 8{ - 3} } " s" \) } {} . (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?
<< Chapter < Page Page > Chapter >>
Practice Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Kinematics. OpenStax CNX. Sep 11, 2015 Download for free at https://legacy.cnx.org/content/col11878/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Kinematics' conversation and receive update notifications?

Ask