To find the horizontal range of the baseball, we need to break down its initial velocity into horizontal and vertical components. The horizontal component of velocity remains constant throughout the motion because there is no external force acting on it.
Given:
Initial velocity (v) = 160 km/hr
Launch angle (θ) = 63 degrees
First, we need to convert the initial velocity from km/hr to m/s since the unit of time in physics calculations is usually in seconds.
1 km/hr = 1000 m / (60 × 60) s = 0.2778 m/s
Therefore, the initial velocity (v) in m/s is 160 × 0.2778 = 44.45 m/s.
Now, we can calculate the horizontal component of velocity (v_x) using the trigonometric function, cosine.
v_x = v × cos(θ)
Substituting the given values, we have:
v_x = 44.45 × cos(63)
Using a calculator, we find that v_x is approximately 19.45 m/s.
Next, we can calculate the horizontal range (R) using the formula:
R = (v_x^2 × sin(2θ)) / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the values into the formula, we have:
R = (19.45^2 × sin(2 × 63)) / 9.8
Calculating this expression, we find that the horizontal range is approximately 133.15 meters.
So, the horizontal range of the baseball, neglecting air resistance, is approximately 133.15 meters.