Question

Тело брошено под углом 60 к горизонту со скоростью 20 м /с. Под каким углом к горизонту движется тело через 1,5 с после начала движения?

Answer 1

v=20   α=60   t=105     β=?

vx=v*cosα   vy=v*sinα

v1y=vy-g*t

tgβ=v1y/vx=(v*sinα-g*t)/(v*cosα)=(20*0.866-10*1.5)/(20*0.5)=0.23

β=arctg0.23=13 градусов

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Answer 2

Calculation of the Angle of Motion

To determine the angle at which the object is moving after 1.5 seconds, we can use the given information. The object was initially thrown at an angle of 60 degrees to the horizontal with a velocity of 20 m/s.

Using the equations of motion, we can calculate the vertical and horizontal components of the velocity after 1.5 seconds.

From source we can see that the initial velocity (v0) is 20 m/s and the angle (θ) is 60 degrees.

The vertical component of the velocity (v_y) can be calculated using the equation:

v_y = v0 * sin(θ)

Substituting the values, we get:

v_y = 20 * sin(60) = 20 * 0.866 = 17.32 m/s

The horizontal component of the velocity (v_x) can be calculated using the equation:

v_x = v0 * cos(θ)

Substituting the values, we get:

v_x = 20 * cos(60) = 20 * 0.5 = 10 m/s

After 1.5 seconds, the vertical component of the velocity remains the same, while the horizontal component changes due to the acceleration of gravity.

The vertical displacement (y) can be calculated using the equation:

y = v_y * t - 0.5 * g * t^2

From source we can see that the time (t) is 1.5 seconds and the acceleration due to gravity (g) is approximately 9.8 m/s^2.

Substituting the values, we get:

y = 17.32 * 1.5 - 0.5 * 9.8 * (1.5)^2 = 25.98 - 11.025 = 14.955 m

The horizontal displacement (x) can be calculated using the equation:

x = v_x * t

Substituting the values, we get:

x = 10 * 1.5 = 15 m

Now, we can calculate the angle (θ') at which the object is moving after 1.5 seconds using the equation:

θ' = arctan(y / x)

Substituting the values, we get:

θ' = arctan(14.955 / 15) = arctan(0.997) ≈ 45 degrees

Therefore, the object is moving at an angle of approximately 45 degrees to the horizontal after 1.5 seconds.

Please note that the calculations are approximate and may vary slightly depending on the specific values used.

Conclusion

After 1.5 seconds, the object is moving at an angle of approximately 45 degrees to the horizontal.