MULTIPLE -CHOICE QUESTION
A baseball is launched from the bat at an angle
θo = 30° what respect to the positive x-axis and with an initial speed of 40 m/s ,and it is caught at the same height from which it is was hit. Assuming ideal projectile motion (positive y-axis upward) ,the velocity of the ball when it is caught is
a. (20.00x+34.64y)m/s
b. (-20.00x+34.64y)m/s
c. (34.64x-20.00y)m/s
d. (34.64x+20.00y)m/s
Vo = 40m/s[30o].
Xo = 40*Cos30 = 34.64 m/s.
Yo = 40*sin30 = 20 m/s.
V = (34.64x + 20.00y)m/s.
To find the velocity of the ball when it is caught, we can analyze the horizontal and vertical components of the velocity separately.
Horizontal component: The initial velocity of the ball in the x-direction is given by Vx = Vo * cos(θo), where Vo is the initial speed and θo is the launch angle.
Vx = 40 m/s * cos(30°)
Vx = 40 m/s * √3/2
Vx = 34.64 m/s (rounded to 2 decimal places)
Vertical component: The initial velocity of the ball in the y-direction is given by Vy = Vo * sin(θo), where Vo is the initial speed and θo is the launch angle.
Vy = 40 m/s * sin(30°)
Vy = 40 m/s * 1/2
Vy = 20 m/s
Since the ball is caught at the same height from which it was launched, the vertical velocity component will be equal in magnitude but opposite in direction to the initial vertical velocity (Vy).
Therefore, the velocity of the ball when it is caught will be the sum of the horizontal and vertical components:
Velocity = Vx * x-direction + Vy * y-direction
Velocity = 34.64x - 20y
So, the correct option is c. (34.64x - 20.00y) m/s.
To find the velocity of the ball when it is caught, we can break the initial velocity into its x and y components. The x component of the velocity (Vx) remains constant throughout the motion since there are no horizontal forces acting on the ball. The y component of the velocity (Vy) changes due to the acceleration of gravity.
Given:
θo = 30°
Initial speed (V0) = 40 m/s
To find Vx and Vy, we use trigonometric functions. The x component can be found using the equation:
Vx = V0 * cos(θo)
Substituting the given values:
Vx = 40 m/s * cos(30°)
Vx = 40 m/s * (√3/2)
Vx = 20√3 m/s
Now, to find Vy, we use the equation:
Vy = V0 * sin(θo)
Substituting the given values:
Vy = 40 m/s * sin(30°)
Vy = 20 m/s
So, the velocity of the ball when it is caught can be represented as a vector combining the x and y components:
Velocity = Vx * î + Vy * ĵ
= 20√3 * î + 20 * ĵ
Comparing this with the given options, we can see that the correct answer is:
a. (20.00x + 34.64y) m/s