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is kicked with an initial velocity of 17 m/s in the horizontal direction and 11 m/s in the vertical direction. (Assume the ball is kicked from the ground.) (a) At what speed (in m/s) does the ball hit the ground? m/s (b) For how long (in s) does the ball remain in the air? (c) What maximum height (in m) is attained by the ball?

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Final answer:

To find the speed at which the ball hits the ground, calculate the resultant velocity by considering the horizontal and vertical motions separately. The time of flight can be found using the equation t = (2 * initial vertical velocity) / acceleration due to gravity. The maximum height is given by the equation h = (initial vertical velocity)^2 / (2 * acceleration due to gravity).

Step-by-step explanation:

To find the speed at which the ball hits the ground, we need to calculate the resultant velocity of the ball when it hits the ground. The horizontal and vertical motions of the ball are independent of each other, so we can consider them separately.

For the horizontal motion, the velocity remains constant at 17 m/s throughout the motion.

For the vertical motion, we can use the equation v^2 = u^2 + 2aS to find the time of flight of the ball. Given that the initial vertical velocity (u) is 11 m/s, and the acceleration due to gravity (a) is -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity), and that the displacement (S) is zero (as the ball returns to the ground), we can solve for the time of flight (t). Once we know the time of flight, we can find the maximum height attained by the ball using the equation h = ut + 0.5at^2.

(a) The speed at which the ball hits the ground is equal to the magnitude of the resultant velocity, which can be found using the Pythagorean theorem. In this case, the horizontal velocity remains constant at 17 m/s, and the vertical velocity decreases due to gravity. So, we have v = sqrt((17 m/s)^2 + (2 * 9.8 m/s^2 * h)), where h is the maximum height.

(b) The time of flight can be found using the equation t = (2 * initial vertical velocity) / acceleration due to gravity.

(c) The maximum height is given by the equation h = (initial vertical velocity)^2 / (2 * acceleration due to gravity).

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