Shooting a Basketball A basketball is shot at a \( 70^{\circ} \) angle with the horizontal direction with an initial speed of \( 10 \mathrm{~m} / \mathrm{sec} \). (a) Find the component form of the initial velocity,

To find the component form of the initial velocity of the basketball, we can use trigonometric functions. The horizontal component \( v_x \) is calculated as \( v_x = v \cdot \cos(\theta) \), and the vertical component \( v_y \) is \( v_y = v \cdot \sin(\theta) \). With an initial speed \( v = 10 \, \text{m/s} \) and an angle \( \theta = 70^{\circ} \): \[ v_x = 10 \cdot \cos(70^{\circ}) \approx 3.42 \, \text{m/s} \] \[ v_y = 10 \cdot \sin(70^{\circ}) \approx 9.35 \, \text{m/s} \] Thus, the component form of the initial velocity is approximately \( (3.42, 9.35) \, \text{m/s} \). Engaging in basketball physics is both fun and enlightening! Did you know that the optimal angle for shooting a basketball is usually around \( 45^{\circ} \)? This allows for the perfect blend of horizontal distance and vertical height. However, shooting at \( 70^{\circ} \) can help players avoid defenders and create a better shooting arc, emphasizing the importance of angles in scoring! When shooting hoops, one common mistake players make is not considering their body positioning. Make sure to align your feet, shoulders, and arms in a straight line towards the basket for greater accuracy. Also, pay attention to your follow-through; it dramatically impacts how the ball leaves your hands. Practicing with proper mechanics makes a big difference in your shot’s success!