Ximena stands near the edge of a cliff 20 m above her friend Javier. If she throws a sandwich to Javier at an angle = 30 below the horizontal and it reaches him in 1.0 s, ignoring air resistance, what was the magnitude of the

sandwich's initial velocity?

A. 20 m/s

B. 30 m/s

C. 5.0 m/s

D. 2.0 m/s

y = Vyot - 1/2gt^2
20 = Vsin30(1) - 1/2(-10_(1^2)
20 = Vsin30 + 5
15 = Vsin30
V = 30 m/s or B.

To solve this problem, we can use the equations of motion in projectile motion. The given information includes the vertical displacement (20m), the time taken (1.0s), and the launch angle (30 degrees below the horizontal).

The first step is to determine the initial vertical velocity component (Vy). We can use the equation:

y = Vyot - 1/2gt^2

where:
y is the vertical displacement (20m)
Vy is the initial vertical velocity component
o is the launch angle below the horizontal (30 degrees)
t is the time taken (1.0s)
g is the acceleration due to gravity (-10m/s^2)

Substituting the given values into the equation:

20 = Vy(1) - 1/2(-10)(1^2)
20 = Vy + 5
Vy = 15

Next, we need to find the magnitude of the initial velocity (V). Since the launch angle is below the horizontal, the initial velocity will have both horizontal and vertical components. The magnitude (V) can be calculated using the equation:

V = Vy / sin(o)

where:
V is the magnitude of the initial velocity
Vy is the initial vertical velocity component
o is the launch angle below the horizontal (30 degrees)

Substituting the given values into the equation:

V = 15 / sin(30)
V ≈ 15 / 0.5
V ≈ 30m/s

Therefore, the magnitude of the sandwich's initial velocity is approximately 30m/s, corresponding to option B.