Question

Тело брошено горизонтально через 5 секунд угол между скоростью и ускорением стал равен 45 градусов.В какой момент времени после броска скорость будет в 2 раза больше начальной скорости?

Answer 1

Решение. Ничего нет интересного в задаче! Просто закон сохранения энергии.
m*g*h=0,5*m*v0^2-0,5*m*(0,5*v0)^2; g*h=0,5*0,75*v0^2; h=(0,375*v0^2)/g; h=(0,375*100)/10=3,75;

Answer 2

Problem Analysis

We are given that a body is thrown horizontally and after 5 seconds, the angle between the velocity and acceleration becomes 45 degrees. We need to determine the time at which the velocity will be twice the initial velocity.

Solution

To solve this problem, we can use the equations of motion for horizontal and vertical motion separately. Since the body is thrown horizontally, the vertical acceleration is zero.

Let's denote the initial velocity as v0 and the time at which the velocity becomes twice the initial velocity as t.

From the given information, we know that after 5 seconds, the angle between the velocity and acceleration becomes 45 degrees. This implies that the vertical component of the velocity is equal to the horizontal component of the velocity at that time.

Using the equation of motion for horizontal motion, we have:

v(t) = v0 + a*t Since the acceleration in the horizontal direction is zero, the equation simplifies to:

v(t) = v0 This means that the horizontal component of the velocity remains constant throughout the motion.

Now, let's consider the vertical motion. Since the vertical acceleration is zero, the equation of motion for vertical motion is:

h(t) = h0 + v0*t + (1/2)*a*t^2 Since the vertical acceleration is zero, the equation simplifies to:

h(t) = h0 + v0*t From the given information, we know that after 5 seconds, the angle between the velocity and acceleration becomes 45 degrees. This implies that the vertical displacement at that time is equal to the horizontal displacement at that time.

Using the equation for vertical displacement, we have:

h(t) = h0 + v0*t Since the vertical displacement is equal to the horizontal displacement, we can equate the two equations:

h(t) = h0 + v0*t = v0*t Simplifying the equation, we get:

h0 = v0*t Now, we can substitute this equation into the equation for vertical displacement:

h(t) = v0*t + v0*t = 2*v0*t Since the vertical displacement is equal to the horizontal displacement, we can equate the two equations:

2*v0*t = v0*t Simplifying the equation, we get:

t = 2 seconds

Therefore, the velocity will be twice the initial velocity 2 seconds after the throw.

Answer

The velocity will be twice the initial velocity 2 seconds after the throw.