Physics, 09.01.2021 03:00 dimontsho4717

A bow has k= 458 N/m. It is pulled back 0.720 m, and used tofire a 0.0925 kg arrow. It hits a bird 24.7 m above the ground. What is the speed of the arrow when it hits?

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Answer from: goodperson21

The final speed of the arrow when it hits the target is 45.63 m/s.

Explanation:

Given;

spring constant of the bow, k = 458 N/m

extension of the bow, x = 0.72 m

mass of the arrow, m = 0.0925 kg

let the initial speed of the arrow after being fired = u

Apply the law of conservation of energy, the elastic potential energy of the bow will be converted to kinetic energy of the arrow.

$\frac{1}{2} kx^2 = \frac{1}{2} mu^2\\\\kx^2 = mu^2\\\\u^2 = \frac{kx^2}{m} \\\\u= \sqrt{\frac{kx^2}{m} } \\\\u = 50.66 \ m/s$

The speed of the arrow when it hits a target 24.7 m above the ground is calculated as;

v² = u² + 2gs

where;

v is the final speed when the arrow hits the target

g is acceleration due to gravity = (-9.8 m/s², upward motion)

v² = 50.66² + 2(-9.8)24.7

v² = 2566.44 - 484.12

v² = 2082.32

v = √2082.32

v = 45.63 m/s

Therefore, the final speed of the arrow when it hits the target is 45.63 m/s.

Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

Answer from: Quest

Two cars collide, lock bumpers and move together after the collision.this collision is known as perfectly inelastic collision.

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A bow has k= 458 N/m. It is pulled back 0.720 m, and used tofire a 0.0925 kg arrow. It hits a bird...

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