Tarzan jumps from a cliff and grabs a vine. He jumps horizontally from the cliff with...

Tarzan jumps from a cliff and grabs a vine. He jumps horizontally from the cliff with initial velocity v₀ at the time t₀. The vine has mass M and length L. Initially, the vine is hanging straight down and is attached at its highest point, O. After the “collision” Tarzan remains attached to the vine with his center of mass at the lower edge of the vine. Tarzan’s mass is m. The vine behaves as a rod attached without friction to the point O. The moment of inertia of a rod around its center of mass is I = (1/12)ML². You can neglect air resistance.

(a) Find Tarzan’s velocity immediately before the collision with the vine (at t₁).

(b) What is the moment of inertia of the vine about the point O?

(c) Show that the angular velocity of the vine (with Tarzan) immediately after the collision is ω₂ = m/((M/3) + m)(v₀/L).

(d) How far up does Tarzan swing?

(e) How high would Tarzan swing if he jumped from twice the height?

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Tarzan wants to swing on a vine across a river. He is standing on a ledge...

Tarzan wants to swing on a vine across a river. He is standing on a ledge above the water's edge and the river is 5m wide. The vine is attached to a tree branch that is 8m directly above the opposite edge of the river. Initially the vine makes a 60 degree angle with the vertical as he is holding it. He swings across starting from rest, but unfortunately the vine breaks when the vine is 20 degrees from the...

An otter jumps horizontally off a cliff with a speed of 2.72 m/s and lands in...

An otter jumps horizontally off a cliff with a speed of 2.72 m/s and lands in the water a horizontal distance of 4.67 m from the edge of the cliff. How high above the water did the otter jumps from? _________ m

Tarzan, who has a mass of 80 kg, holds onto the end of a vine that...

Tarzan, who has a mass of 80 kg, holds onto the end of a vine that is at a 13 ∘ angle from the vertical. He steps off his branch and, just at the bottom of his swing, he grabs onto his chimp friend Cheetah, whose mass is 50 kg. What is the maximum angle the rope reaches as Tarzan swings to the other side? Express your answer in degrees.

Tarzan, who has a mass of 85 kg, holds onto the end of a vine that...

Tarzan, who has a mass of 85 kg, holds onto the end of a vine that is at a 13 ∘ angle from the vertical. He steps off his branch and, just at the bottom of his swing, he grabs onto his chimp friend Cheetah, whose mass is 30 kg. What is the maximum angle the rope reaches as Tarzan swings to the other side?

A cannonball is fired horizontally from the top of a cliff. The cannon is at height...

A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 100m above ground level, and the ball is fired with initial horizontal speed v0=0. Assume acceleration due to gravity to be g = 9.80 m/s2. a)Assume that the cannon is fired at time t=0 and that the cannonball hits the ground at time tg. What is the y position of the cannonball at the time tg/2? b) Given that the projectile lands...

Jane is looking for Tarzan is runnning at top speed of 5.3 m/s. She grabs a...

Jane is looking for Tarzan is runnning at top speed of 5.3 m/s. She grabs a vine hanging vertically from a tall tree. How high can she swing

A bungee jumper of mass 110 kg jumps from a cliff of height 120m. The massless...

A bungee jumper of mass 110 kg jumps from a cliff of height 120m. The massless relaxed bungee cord has a length of 15 m. Ignore the height of the body of the jumper. K=125N/m. (a) Find the velocity of the jumper right before the bungee starts to stretch. (b) Find the distance the cord stretches. Please explain the steps. Thank you!

On planet #3, you fire a projectile horizontally from the edge of a vertical cliff 34.4...

On planet #3, you fire a projectile horizontally from the edge of a vertical cliff 34.4 m above the ground, with an initial speed of 72.6 m/s. The projectile lands 63.5 m away from the base of the cliff. What is the value of g for planet #3? 89.93 m/s^2 44.97 m/s^2 282.83 m/s^2 28.51 m/s^2

A ball is kicked horizontally with 15 m/s initial speed from a cliff. The ball lands...

A ball is kicked horizontally with 15 m/s initial speed from a cliff. The ball lands 75 m away from the base of the cliff (R = 75m). What is the height of the cliff? What is the hitting velocity (the velocity of the ball before it hits the ground)? What is the total time of flight?

A ball is thrown horizontally off the edge of a cliff with an initial speed of...

A ball is thrown horizontally off the edge of a cliff with an initial speed of 20 m/s . how long does it take for the ball to fall to the ground 86.3 m below? .How long would it take for the ball to reach the ground 86.3 m below if it were dropped from rest off the cliff edge ? . how long would it take the ball to fall to the ground 86.3 m below if it were...

Subjects