What is the resultant velocity of a 30 m/s at angle of 45° to the horizontal?
9m/s
horizontal component of velocity = 30 cos 45
vertical component of velocity = 30 sin 45
since sin 45 = cos 45 = about .707, the same
was up
To find the resultant velocity of an object moving at an angle to the horizontal, we can use vector addition.
Given the initial velocity magnitude (speed) of 30 m/s and an angle of 45° to the horizontal, we can break down the velocity into its horizontal and vertical components.
The horizontal component (Vx) represents the velocity in the x-axis, parallel to the ground, and can be determined using the formula:
Vx = V * cos(θ)
where V is the magnitude of the velocity (30 m/s) and θ is the angle with respect to the horizontal (45°).
Vx = 30 m/s * cos(45°)
Vx = 30 m/s * (√2 / 2)
Vx ≈ 21.2 m/s
The vertical component (Vy) represents the velocity in the y-axis, perpendicular to the ground, and can be determined using the formula:
Vy = V * sin(θ)
Vy = 30 m/s * sin(45°)
Vy = 30 m/s * (√2 / 2)
Vy ≈ 21.2 m/s
Now, to find the resultant velocity, we can use the Pythagorean theorem:
Resultant velocity (Vr) = √(Vx^2 + Vy^2)
Vr = √((21.2 m/s)^2 + (21.2 m/s)^2)
Vr ≈ 29.9 m/s
Therefore, the resultant velocity of an object moving at a speed of 30 m/s at an angle of 45° to the horizontal is approximately 29.9 m/s.