The speed of the boy sliding down the slide is determined by the principle of conservation of energy. At the top of the slide, all of the boy's energy is potential energy, which is given by the formula PE = mgh, where m is mass, g is gravity, and h is height. As he slides down, this potential energy is converted into kinetic energy, which is given by the formula KE = 0.5mv^2, where m is mass and v is velocity.

Setting these two equations equal to each other (since energy is conserved), we get:

mgh = 0.5mv^2

We can cancel out the mass on both sides, since it doesn't change:

gh = 0.5v^2

If we want to double the speed (v), we have to quadruple the kinetic energy (since v^2 is in the formula for kinetic energy). Therefore, we need to quadruple the potential energy, which means we need to quadruple the height of the slide.

So, the factor by which the parents should increase the height of the slide is 4.0.

Question

The speed of the boy sliding down the slide is determined by the principle of conservation of energy. At the top of the slide, all of the boy's energy is potential energy, which is given by the formula PE = mgh, where m is mass, g is gravity, and h is height. As he slides down, this potential energy is converted into kinetic energy, which is given by the formula KE = 0.5mv^2, where m is mass and v is velocity.

Setting these two equations equal to each other (since energy is conserved), we get:

mgh = 0.5mv^2

We can cancel out the mass on both sides, since it doesn't change:

gh = 0.5v^2

If we want to double the speed (v), we have to quadruple the kinetic energy (since v^2 is in the formula for kinetic energy). Therefore, we need to quadruple the potential energy, which means we need to quadruple the height of the slide.

So, the factor by which the parents should increase the height of the slide is 4.0.

Knowee AI · Accepted Answer

The speed of the boy sliding down the slide is determined by the principle of conservation of energy. At the top of the slide, all of the boy's energy is potential energy, which is given by the formula PE = mgh, where m is mass, g is gravity, and h is height. As he slides down, this potential energy is converted into kinetic energy, which is given by the formula KE = 0.5mv^2, where m is mass and v is velocity.

Setting these two equations equal to each other (since energy is conserved), we get:

mgh = 0.5mv^2

We can cancel out the mass on both sides, since it doesn't change:

gh = 0.5v^2

If we want to double the speed (v), we have to quadruple the kinetic energy (since v^2 is in the formula for kinetic energy). Therefore, we need to quadruple the potential energy, which means we need to quadruple the height of the slide.

So, the factor by which the parents should increase the height of the slide is 4.0.

A boy slides down a frictionless slide. If the boy wants to go twice as fast at the bottom of the slide, by what factor should his parents increase the height of the slide? 4.0 0.50 2.0 3.0

Question

Solution

Similar Questions

Upgrade your grade with Knowee