To find the angle of the plane with respect to the horizontal, we can use the kinematic equations of motion.
Let's start by finding the acceleration of the block.
We can use the equation:
v = u + at,
where:
v = final velocity = 4.37 m/s,
u = initial velocity = 1.13 m/s,
a = acceleration,
t = time interval = 1.2 s.
Rearranging the equation to solve for a, we get:
a = (v - u) / t.
Substituting the given values, we have:
a = (4.37 m/s - 1.13 m/s) / 1.2 s.
a = 3.24 m/s / 1.2 s.
a = 2.7 m/s².
Now, we can find the angle using the equation:
a = g * sin(θ),
where:
g = acceleration due to gravity = 9.8 m/s²,
θ = angle of the plane.
Rearranging the equation to solve for θ, we have:
θ = arcsin(a / g).
Substituting the known values, we get:
θ = arcsin(2.7 m/s² / 9.8 m/s²).
Using a calculator, we find:
θ ≈ 0.2776 radians.
To convert radians to degrees, we multiply by 180/Ï€:
θ ≈ 0.2776 * 180/π ≈ 15.91 degrees.
Therefore, the angle of the plane with respect to the horizontal is approximately 15.91 degrees.