Question

Во сколько раз надо увеличить начальную скорость брошенного вертикально вверх тела, чтобы высота подъёма увеличилась в 4 раза?

Answer 1

Eп = Ек
mgh = mVо^2/2
gh = Vо^2/2
h ~ Vо^2
4h ~ (2Vо)^2
в ДВА раза надо увеличить начальную скорость

Answer 2

Calculation of the Required Increase in Initial Velocity

To determine the factor by which the initial velocity of a vertically thrown object needs to be increased in order to increase the maximum height by a factor of 4, we can use the equations of motion.

The equation for the maximum height reached by a vertically thrown object is given by:

h = (v0^2) / (2g)

where: - h is the maximum height - v0 is the initial velocity - g is the acceleration due to gravity

We want to find the factor by which the initial velocity needs to be increased, so let's call this factor k.

If we increase the initial velocity by a factor of k, the new initial velocity will be kv0. Substituting this into the equation for maximum height, we get:

4h = (kv0^2) / (2g)

Simplifying the equation, we have:

4(v0^2) / (2g) = (kv0^2) / (2g)

Cancelling out the common terms, we get:

4 = k

Therefore, the initial velocity needs to be increased by a factor of 4 in order to increase the maximum height by a factor of 4.

Answer

To increase the maximum height by a factor of 4, the initial velocity of the vertically thrown object needs to be increased by a factor of 4