Question

In your first semester physics course, you will learn the subject of Kinematics which deals with Projectile Motion. For this problem we’ll be looking at the individual horizontal and vertical components of an object. The parametric equations for the motion of a baseball hit at an angle θ is given by:

x(t)=(v0 cos (θ))t
y(t)=h+(v0sin (θ))t- 1/2 gt²

Where v_0 is the exit velocity, θ is the exit angle, h is the initial vertical height, and g is the acceleration due to gravity.
a. Suppose a baseball is hit 3ft above the ground, with an exit angle of 30° , and an exit velocity of 130ग/. Record the parametric equations for the baseball below. Assume g=32 (ft)/s²)

Answer 1

Parametric equations for projectile motion of a hitted baseball with initial height, exit angle and velocity are formulated, highlighting the constant horizontal velocity and the linearly changing vertical velocity due to gravity.

Step-by-step explanation:

The question involves projectile motion, a key concept in Kinematics within a Physics course. In the given scenario, a baseball is hit with an initial vertical height (h) of 3 feet, an exit angle (θ) of 30°, and an exit velocity (v0) of 130 feet per second. With g equal to 32 feet per second squared, the parametric equations for the baseball's motion are:

x(t) = (v0 × cos(θ)) × t

y(t) = h + (v0 × sin(θ)) × t - ½ × g × t²

Plugging in the known values:

x(t) = (130 × cos(30°)) × t

y(t) = 3 + (130 × sin(30°)) × t - ½ × 32 × t²

The x-component of velocity (horizontal direction) does not change over time since there is no horizontal acceleration (ax = 0). Thus, the horizontal velocity graph will be a horizontal line at 5 m/s from the time the ball is launched until it hits the ground. For the y-component of velocity (vertical direction), the velocity will decrease linearly until it reaches zero at the peak of the trajectory, then increase in the negative direction as the ball descends to the ground.