A body with a mass of 1 kg, thrown at an angle a to the horizon, at a height of 1.4m had a speed of 6m / s

| September 9, 2021 | education

A body with a mass of 1 kg, thrown at an angle a to the horizon, at a height of 1.4m had a speed of 6m / s. The minimum value of the impulse for the entire time of movement is 4 kg * m / s. Find the angle a

Problem data: m (the mass of the thrown body) = 1 kg; h (considered height) = 1.4 m; V (speed at the considered height) = 6 m / s; Pmin (minimum impulse, highest lifting point) = 4 kg * m / s.

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

1) Speed at the highest lifting point: V0x = V0 * cosα = Рmin / m, whence V0 = Рmin / (m * cosα).

2) The law of conservation of energy: m * V0 ^ 2/2 = m * g * h + m * V ^ 2/2.

V0 ^ 2 = 2m * g * h + m * V ^ 2.

(Pmin / (m * cosα)) ^ 2 = 2m * g * h + m * V ^ 2.

(4 / (1 * cosα)) ^ 2 = 2 * 1 * 10 * 1.4 + 1 * 6 ^ 2.

(4 / cosα) ^ 2 = 64.

4 / cosα = 8.

α = arccos (4/8) = arccos 0.5 = 60º.

Answer: The throw angle is 60º.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.