IP A jogger runs with a speed of 3.10{\rm m/s} in a direction 25.0{^\circ} above the x axis. Find the x and y components of the jogger's velocity.
x: 3.10 cos25° = 2.809 m/s
y: 3.10 sin25° = 1.310 m/s
To find the x and y components of the jogger's velocity, we can use trigonometry.
The jogger's velocity can be split into two components: the x-component and the y-component.
Given:
Speed of the jogger (v) = 3.10 m/s
Angle above the x-axis (θ) = 25.0°
To find the x-component (vx) of the velocity, we can use the cosine function:
vx = v * cos(θ)
Plugging in the values:
vx = 3.10 m/s * cos(25.0°)
Using a calculator, we find that:
vx ≈ 2.805 m/s
To find the y-component (vy) of the velocity, we can use the sine function:
vy = v * sin(θ)
Plugging in the values:
vy = 3.10 m/s * sin(25.0°)
Using a calculator, we find that:
vy ≈ 1.317 m/s
Therefore, the x-component of the jogger's velocity is approximately 2.805 m/s and the y-component is approximately 1.317 m/s.
To find the x and y components of the jogger's velocity, we can use trigonometry. Since the jogger is running at an angle of 25.0 degrees above the x-axis, we can decompose the velocity into its x and y components using trigonometric functions.
The x component of the velocity, Vx, can be found using the formula:
Vx = V * cos(θ)
where V is the magnitude of the velocity (3.10 m/s) and θ is the angle (25.0 degrees).
Calculating Vx:
Vx = 3.10 m/s * cos(25.0°)
Vx ≈ 2.80 m/s
The y component of the velocity, Vy, can be found using the formula:
Vy = V * sin(θ)
Calculating Vy:
Vy = 3.10 m/s * sin(25.0°)
Vy ≈ 1.34 m/s
Therefore, the x component of the jogger's velocity is approximately 2.80 m/s and the y component is approximately 1.34 m/s.