A firecracker explodes, sending pieces of equal mass in three directions as shown in the diagram. Angle θ is 14 degrees, and angle ϕ is 30 degrees. Assume that the firecracker is initially at rest, and take upward and rightward as the positive directions.

What are the components of the right-hand piece’s velocity?

Horizontal component:

What is the answer? I need it.

To find the horizontal component of the right-hand piece's velocity, we need to use trigonometry.

We can use the angle θ to find the horizontal component.

Using the given angle θ = 14 degrees, we can use cosine function to find the horizontal component of velocity.

cos(θ) = Adjacent / Hypotenuse

cos(14 degrees) = Horizontal component / Velocity

Rearranging the equation, we can solve for the horizontal component of velocity:

Horizontal component = cos(14 degrees) * Velocity

We are given that the firecracker is initially at rest, which means the velocity is zero. Therefore, the horizontal component of the right-hand piece's velocity is zero.

To determine the horizontal component of the right-hand piece's velocity, we need to calculate the component of the velocity vector that points in the horizontal direction.

To do this, we can use trigonometry. Given that the angle θ is 14 degrees and assuming that the rightward direction is considered positive, the horizontal component can be determined using the formula:

Horizontal component = velocity * cos(θ)

Since the firecracker is initially at rest, the velocity of each piece will be the same. Therefore, to find the horizontal component, we need to know the magnitude of the velocity. Unfortunately, the magnitude of the velocity is not given in the question, so we cannot provide a specific numerical value for the horizontal component.

However, if we have the magnitude of the velocity, we can substitute it into the formula to determine the horizontal component.