Question

Мячик массой 100 г, брошенный вертикально вверх, вернулся обратно через 6 с. Определите импульс мяча в момент броска и в верхней точке.

Answer 1

В верхней точке он (импульс) равен нулю, так как скорость там равна нулю, а по определению P=m*v 
вернулся через 6 секунд, значит наверху был через 3 секунды (из симметрии). 
Тогда начальную скорость можно найти как падение с нулевой начальной скоростью из верхней точки 
v=g*t=9.81*3=29.43 м/c 
и начальный импульс тогда Pнач=0.1*29.43=2.943 кг*м/c

Answer 2

Impulse of the Ball at the Moment of Throw

To determine the impulse of the ball at the moment of throw, we need to use the equation for impulse:

Impulse = Change in momentum

The momentum of an object is given by the product of its mass and velocity:

Momentum = mass × velocity

Since the ball is thrown vertically upwards, its velocity at the moment of throw is the initial velocity. Let's assume the initial velocity is v0.

Therefore, the momentum of the ball at the moment of throw is:

Momentum = mass × v0

Given that the mass of the ball is 100 g (or 0.1 kg), we can calculate the impulse using the given information.

Now, let's find the value of the initial velocity v0 using the equation for displacement in vertical motion:

Displacement = Initial velocity × time + (1/2) × acceleration × time^2

Since the ball returns back to its initial position, the displacement is zero. The acceleration due to gravity is approximately 9.8 m/s^2.

Substituting the values, we get:

0 = v0 × 6 + (1/2) × (-9.8) × 6^2

Simplifying the equation, we find:

v0 × 6 = (1/2) × 9.8 × 36

v0 × 6 = 176.4

v0 = 176.4 / 6

v0 ≈ 29.4 m/s

Now that we have the value of the initial velocity, we can calculate the impulse:

Impulse = mass × v0

Impulse = 0.1 kg × 29.4 m/s

Impulse ≈ 2.94 kg·m/s

Therefore, the impulse of the ball at the moment of throw is approximately 2.94 kg·m/s.

Impulse of the Ball at the Highest Point

To determine the impulse of the ball at the highest point, we need to consider the fact that the velocity of the ball at the highest point is zero. This means that the change in momentum is equal to the negative of the momentum at the moment of throw.

Since the momentum at the moment of throw is given by:

Momentum = mass × v0

The impulse at the highest point is:

Impulse = -mass × v0

Substituting the values, we get:

Impulse = -0.1 kg × 29.4 m/s

Impulse ≈ -2.94 kg·m/s

Therefore, the impulse of the ball at the highest point is approximately -2.94 kg·m/s.

Please note that the negative sign indicates that the direction of the impulse is opposite to the direction of the initial throw.