A baseball is hit and moves initially at an angle of 35.0
to the
horizontal ground with a velocity of 25.0 m/s.
(a) What are the vertical and horizontal components of the initial
velocity?
(b) How long will the ball be in the air?
(c) What is the range?
a. Vo = 25m/s[35o]
Xo = 25*Cos35 =
Yo = 25*sin35 =
b. See previous prob.
c. See previous prob.
To find the answers to these questions, you will need to use basic kinematic equations and trigonometry. Let's break down the problem step-by-step.
(a) Finding the vertical and horizontal components of the initial velocity:
The vertical component (Vy) of the initial velocity can be found using the formula:
Vy = V * sin(theta)
where V is the magnitude of the initial velocity and theta is the angle with respect to the horizontal.
Substituting the given values:
Vy = 25.0 m/s * sin(35.0°)
Using a scientific calculator, calculate the value of sin(35.0°) and multiply it by 25.0 m/s to find the vertical component of the initial velocity.
Similarly, the horizontal component (Vx) of the initial velocity can be found using the formula:
Vx = V * cos(theta)
Substituting the given values:
Vx = 25.0 m/s * cos(35.0°)
Using a scientific calculator, calculate the value of cos(35.0°) and multiply it by 25.0 m/s to find the horizontal component of the initial velocity.
(b) Finding the time the ball will be in the air:
First, find the time it takes for the ball to reach its maximum height using the formula:
t = Vy / (g)
where t is the time, Vy is the vertical component of the initial velocity, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values:
t(max) = Vy / (g)
Next, find the total time the ball will be in the air by doubling the time it takes to reach the maximum height:
t(total) = 2 * t(max)
(c) Finding the range:
The range can be calculated using the formula:
R = Vx * t(total)
where R is the range and Vx is the horizontal component of the initial velocity.
substituting the given values to the formula, using the previously result of the time it takes it be in the air (t(total)), and the horizontal component Vx, we can calculate the range.
By following these steps and performing the necessary calculations, you will be able to find the vertical and horizontal components of the initial velocity, the time the ball will be in the air, and the range.