an object is shot from the ground at an angle of 35 degrees with a speed of 50m/s. what are the x and y components of its velocity initially at the top of its path and just before it hits the ground?

To determine the x and y components of the object's velocity initially at the top of its path and just before it hits the ground, we can use the following equations:

1. For the initial velocity at the top of the path (Vx_initial, Vy_initial):
- Vx_initial = V_initial * cos(θ)
- Vy_initial = V_initial * sin(θ)

2. For the velocity just before the object hits the ground (Vx_final, Vy_final):
- Vx_final = V_initial * cos(θ)
- Vy_final = -V_initial * sin(θ)

Now, let's calculate the components one by one:

1. Initial Components at the Top of the Path:
- V_initial = 50 m/s (given)
- θ = 35 degrees (given)

Using the equations:
- Vx_initial = V_initial * cos(θ)
= 50 * cos(35°)
≈ 41.01 m/s

- Vy_initial = V_initial * sin(θ)
= 50 * sin(35°)
≈ 28.43 m/s

Therefore, at the top of its path, the x-component of its velocity (Vx_initial) is approximately 41.01 m/s, and the y-component (Vy_initial) is approximately 28.43 m/s.

2. Final Components Just Before Hitting the Ground:
- V_initial = 50 m/s (given)
- θ = 35 degrees (given)

Using the equations:
- Vx_final = V_initial * cos(θ)
= 50 * cos(35°)
≈ 41.01 m/s

- Vy_final = -V_initial * sin(θ) (negative sign due to downward direction)
= -50 * sin(35°)
≈ -28.43 m/s

Therefore, just before it hits the ground, the x-component of its velocity (Vx_final) is approximately 41.01 m/s, and the y-component (Vy_final) is approximately -28.43 m/s.