Basketball thrown straight up from the ground

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In summary, a basketball thrown straight up from the ground follows a parabolic trajectory influenced by gravity. Initially, it ascends until its velocity decreases to zero at the peak of its flight, after which it descends back to the ground. The height reached and the time spent in the air depend on the initial speed of the throw.
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yashboi123
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Substandard Post Quality -- Please always type your work into the forum.
Homework Statement
Basketball thrown straight up from the ground, Vo = 5m/s, what equations correctly finds position y(t), velocity of the basketball vy(t), and acceleration
Relevant Equations
kinematic equations
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Would greatly appreciate an explanation on this question, not sure I even understand what they're asking.
 
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I assume that the scribblings in red are your attempt at a solution.

They are giving you three equations, which are too blurred to read, and are asking you to find which one(s) correctly describe(s) the physical situation of throwing the ball straight up in the air.

You say that the relevant equations are "the kinematic equations." What are they and how would you adapt them to this particular situation? Please post the answers in a legible form, ideally using LaTeX. Click on the link "LaTeX Guide" (lower left) to learn how.
 
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FAQ: Basketball thrown straight up from the ground

What factors determine the maximum height a basketball reaches when thrown straight up from the ground?

The maximum height a basketball reaches is determined by the initial velocity at which it is thrown, the acceleration due to gravity (approximately 9.81 m/s² on Earth), and air resistance. The initial velocity is the most crucial factor, as a higher initial velocity will result in a higher maximum height.

How can you calculate the time it takes for the basketball to reach its maximum height?

The time it takes for the basketball to reach its maximum height can be calculated using the formula: \( t = \frac{v_0}{g} \), where \( v_0 \) is the initial velocity and \( g \) is the acceleration due to gravity (9.81 m/s²). This formula assumes no air resistance and that the motion occurs near the Earth's surface.

What is the velocity of the basketball at its maximum height?

At its maximum height, the velocity of the basketball is zero. This is because the upward motion has decelerated to the point where it momentarily stops before reversing direction and beginning to fall back down due to gravity.

How does air resistance affect the motion of the basketball when thrown straight up?

Air resistance opposes the motion of the basketball, reducing its upward velocity and, consequently, the maximum height it can reach. It also affects the time it takes for the basketball to ascend and descend, generally causing the basketball to take longer to return to the ground compared to a scenario without air resistance.

What is the total time the basketball spends in the air before returning to the ground?

The total time the basketball spends in the air can be calculated by doubling the time it takes to reach its maximum height. Using the formula \( t = \frac{v_0}{g} \) for the ascent, the total time in the air is \( 2t = \frac{2v_0}{g} \). This calculation assumes no air resistance and that the motion occurs near the Earth's surface.

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