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A basketball player throws a ball at an angle of 30° above the horizontal. If the ball has an initial velocity of 29.4 m/s, how far does it travel?

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Final answer:

To find the distance traveled by a basketball, we can separate the horizontal and vertical motion. Using vertical motion equation, we can find the time it takes for the ball to hit the ground. Then, using horizontal motion equation, we can determine the horizontal distance traveled.

Step-by-step explanation:

In projectile motion, the horizontal and vertical motion of an object can be analyzed separately. In this case, we will first determine the time it takes for the ball to hit the ground. Using the vertical motion equation, we can calculate the time:

h=vt+1/2gt^2

where h is the initial vertical displacement, v is the vertical component of the initial velocity, g is the acceleration due to gravity, and t is the time.

By substituting the given values into the equation, we can solve for t. Once we have the time, we can determine the horizontal distance using the horizontal motion equation:

d=vt

where d is the horizontal distance and v is the horizontal component of the initial velocity. Utilizing trigonometry, we can find the horizontal and vertical components of the initial velocity:

v_horizontal = v * cos(theta)

v_vertical = v * sin(theta)

By substituting the values into the equation, we can solve for the horizontal distance.

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