A tennis player hits a ball at ground level, giving it an initial velocity of 24 m/s at 57 degrees above the horizontal. (a) what are the horizontal and verticla components of the ball;s initial velocity? (b) how high above the ground does the ball go? (c) How long does it take the ball to reach its maximum height? (d) What are the ball;s velocity and acceleration at its highest point? (e) for how long a time is the ball in the air? (f) When this ball lands on the court, how far is it from the place where it was hit?

Where do I even start here?

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To solve this problem, we can break it down into smaller steps and use basic kinematic equations. Let's start by answering each part of the question one by one:

(a) To find the horizontal and vertical components of the ball's initial velocity, we can use trigonometry. The horizontal component is given by:

Horizontal component = initial velocity * cos(angle)

Vertical component = initial velocity * sin(angle)

In this case, the initial velocity is 24 m/s, and the angle is 57 degrees. Using these values, we can calculate the horizontal and vertical components.

(b) To determine how high above the ground the ball goes, we need to find the maximum height reached by the ball. We can use the vertical motion equation:

Vertical displacement = (initial vertical velocity^2) / (2 * acceleration due to gravity)

Here, the initial vertical velocity is the vertical component of the ball's initial velocity, and the acceleration due to gravity is approximately 9.8 m/s^2.

(c) The time taken for the ball to reach its maximum height can be found using the vertical motion equation:

Time = initial vertical velocity / acceleration due to gravity

(d) At its highest point, the ball's velocity will be entirely horizontal, and its acceleration will be entirely due to gravity (straight down). Therefore, the ball's velocity at its highest point is equal to the horizontal component of its initial velocity. The ball's acceleration at its highest point will be equal to the acceleration due to gravity.

(e) The total time the ball remains in the air can be calculated by doubling the time it takes to reach its maximum height. This is because the time taken to reach the maximum height is the same as the time taken to fall back down.

(f) To determine how far the ball lands from the place where it was hit, we can use the horizontal motion equation:

Horizontal displacement = horizontal component of initial velocity * total time in the air

By using these steps, you can find the answers to each part of the problem. Divide the problem into smaller sub-problems and follow the equations mentioned earlier to get the required values.