Question

A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30° above the horizontal. How far from the throwing point will the ball attain its original level (maximum Range)?

Answer 1

Let's first find the time that the baseball takes to reach the maximum height from the kinematic equation:

$$v_y=v_0sin\theta-gt_{rise},$$ $$0=v_0sin\theta-gt_{rise},$$ $$t_{rise}=\dfrac{v_0sin\theta}{g}.$$

Then, we can find the total flight time of the baseball:

$$t=2t_{rise}=\dfrac{2v_0sin\theta}{g}.$$

Finally, we can find the maximum range of the baseball from the kinematic equation:

$$R=v_0tcos\theta=v_0cos\theta\dfrac{2v_0sin\theta}{g}=\dfrac{v_0^2sin2\theta}{g},$$ $$R=\dfrac{(100\ \dfrac{m}{s})^2\cdot sin2\cdot 30^{\circ}}{9.8\ \dfrac{m}{s^2}}=884\ m.$$

Answer:

$R=884\ m.$