A spider crawling across a table leaps onto a magazine blocking its path. The initial velocity of the spider is 0.860 m/s at an angle of 33.6° above the table, and it lands on the magazine 0.0790 s after leaving the table. Ignore air resistance. How thick is the magazine? Express your answer in millimeters.

Y = ver. = 0.860sin33.6 = 0.4759m/s.

d = Vi*t + 0.5gt^2,
d=0.4759*0.0790 + 0.5*(-9.8)(0.0790)^2,
d = 0.037596 - 0.0305809,
d = 7.02*10^-3m = 7.02mm thick.

To find the thickness of the magazine, we can use the vertical motion equation:

d = (V_iy)(t) + (0.5)(a)(t^2)

Where:
d = the vertical distance traveled
V_iy = the initial vertical component of velocity
t = time
a = acceleration

Since there is no vertical acceleration (ignoring air resistance), the equation simplifies to:

d = (V_iy)(t)

Given that V_iy = 0.860 m/s * sin(33.6°) and t = 0.0790 s, we can plug in the values to find d.

d = (0.860 m/s * sin(33.6°))(0.0790 s)
d ≈ 0.4406 m

To convert the distance to millimeters, we multiply by 1000 since 1 meter = 1000 millimeters:

d ≈ 0.4406 m * 1000 = 440.6 mm

Therefore, the thickness of the magazine is approximately 440.6 millimeters.

To find the thickness of the magazine, we can use the kinematic equations of motion. We know the initial velocity (u) and the time taken (t) to land on the magazine. The key here is to find the vertical displacement (Δy) of the spider, which will help us determine the thickness of the magazine.

1. Find the vertical displacement (Δy):
We can use the equation of motion:
Δy = ut + (1/2)at^2

Since the initial velocity is in the vertical direction, we can use the vertical component of the initial velocity (uy = u * sinθ).
Δy = (u * sinθ) * t + (1/2) * (-9.8) * t^2
The acceleration, -9.8 m/s^2, is due to gravity.

Substituting the given values:
Δy = (0.860 * sin33.6°) * 0.0790 + (1/2) * (-9.8) * (0.0790)^2

Calculating Δy:
Δy ≈ 0.352 m

2. Convert the thickness to millimeters:
Since 1 meter = 1000 millimeters, we can convert the thickness from meters to millimeters.
Thickness = Δy * 1000

Calculating the thickness:
Thickness ≈ 0.352 * 1000
Thickness ≈ 352 mm

Therefore, the thickness of the magazine is approximately 352 millimeters.