An outfielder throws a 0.150 kg baseball at a speed of 26.0 m/s and an initial angle of 30.0°. What is the kinetic energy of the ball at the highest point of its motion?

m = .150kg

v = 40m/s
Theta = 30 degrees

Vh = 40*cos(30)>>>>Vh = 34.64m/s
KE = (1/2)(.150kg)(34.64)^2>>>>KE = 90J

To find the kinetic energy of the ball at the highest point of its motion, we'll need to break down the motion into horizontal and vertical components.

First, let's find the vertical component of the velocity. We can use the initial velocity and the angle of projection to find the vertical component of the velocity using the following formula:

Vertical velocity (Vy) = Initial velocity (V) * sin(angle)

Vy = 26.0 m/s * sin(30°)
Vy ≈ 13.0 m/s

Since the ball reaches its highest point, the vertical velocity at that point will be zero.

Now, let's find the kinetic energy at the highest point. The kinetic energy is given by the formula:

Kinetic energy (KE) = 1/2 * mass (m) * velocity (v)^2

At the highest point, the velocity of the ball is only the horizontal component of the velocity. So, in this case, the velocity will be the horizontal component, which is:

Horizontal velocity (Vx) = Initial velocity (V) * cos(angle)

Vx = 26.0 m/s * cos(30°)
Vx ≈ 22.6 m/s

Now, we can calculate the kinetic energy using the mass of the ball (m = 0.150 kg) and the horizontal velocity (Vx):

KE = 1/2 * m * Vx^2
KE = 1/2 * 0.150 kg * (22.6 m/s)^2
KE ≈ 45.92 J

Therefore, the kinetic energy of the baseball at the highest point of its motion is approximately 45.92 Joules.

To find the kinetic energy of the ball at the highest point of its motion, we first need to determine the vertical component of the velocity at that point.

Step 1: Find the vertical component of the initial velocity.

Given:
Initial velocity (v) = 26.0 m/s
Initial angle (θ) = 30.0°

The vertical component of the initial velocity can be found using the formula:
Vertical velocity (vy) = v * sin(θ)

Substituting the given values:
vy = 26.0 m/s * sin(30.0°)

Using a calculator:
vy ≈ 13.0 m/s

Step 2: Find the kinetic energy at the highest point.

At the highest point of the ball's motion, its vertical velocity will be zero. However, the ball still has horizontal velocity. Since kinetic energy depends on velocity squared, we can sum the square of the horizontal and vertical velocities to find the total kinetic energy. Since the vertical velocity is zero at the highest point, the kinetic energy will only be due to the horizontal velocity.

Kinetic energy = 1/2 * m * (horizontal velocity)^2

Given:
Mass of the baseball (m) = 0.150 kg
Horizontal velocity (vx) = v * cos(θ)

Substituting the given values:
Horizontal velocity (vx) = 26.0 m/s * cos(30.0°)

Using a calculator:
vx ≈ 22.5 m/s

Now we can calculate the kinetic energy at the highest point:
Kinetic energy = 1/2 * 0.150 kg * (22.5 m/s)^2

Using a calculator:
Kinetic energy ≈ 56.3 J

Therefore, the kinetic energy of the ball at the highest point of its motion is approximately 56.3 Joules.