Ximena stands near the edge of a cliff 20 ma bove her friend Javier. If she throws a ball 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?
(use g = 10 m/s2)
To find the magnitude of the initial velocity of the ball, we can use the principles of projectile motion.
First, we need to find the horizontal and vertical components of the ball's initial velocity separately.
Given:
- The angle below the horizontal at which the ball is thrown, θ = 30 degrees.
- The time it takes for the ball to reach Javier, t = 1.0 s.
- The acceleration due to gravity, g = 10 m/s^2.
Step 1: Finding the horizontal component (Vx):
The horizontal component of the ball's initial velocity remains constant throughout the motion.
Using the formula: Vx = (horizontal displacement) / (time)
The horizontal displacement is zero because the ball is thrown from Ximena to Javier horizontally. Therefore, Vx = 0.
Step 2: Finding the vertical component (Vy):
The vertical component of the ball's initial velocity changes due to the acceleration of gravity.
Using the formula: Vy = gt
Substituting the given values: Vy = (10 m/s^2) * (1.0 s)
Vy = 10 m/s
Step 3: Finding the magnitude of the initial velocity (V):
The magnitude of the initial velocity can be found using the Pythagorean theorem, which states that the sum of the squares of the two perpendicular components is equal to the square of the hypotenuse (the magnitude of the initial velocity).
Using the formula: V = √(Vx^2 + Vy^2)
Substituting the values: V = √((0 m/s)^2 + (10 m/s)^2)
V = √(0 + 100) m/s
V ≈ 10 m/s
Therefore, the magnitude of the ball's initial velocity is approximately 10 m/s.