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A ball is rolled off a 250 m cliff with a constant horizontal velocity of 40 m/s. Calculate the following:

1. Vertical Final Velocity: _________
2. Horizontal Displacement: _________
3. Vertical Time: _________
4. Horizontal Time: _________

Options:

A) 0 m/s, 200 m, 5 s, 6.25 s
B) 9.8 m/s, 200 m, 5 s, 6.25 s
C) 0 m/s, 250 m, 5 s, 6.25 s
D) 9.8 m/s, 250 m, 5 s, 6.25 s

Answer :

Final answer:

The vertical final velocity is 9.8 m/s, the horizontal displacement is 200 m, the vertical time is 5 s, and the horizontal time is 5 s.

Explanation:

To find the vertical final velocity, we need to determine the time it takes for the ball to fall off the cliff. We can use the equation: h = 1/2 * g * t^2, where h is the height of the cliff (250 m) and g is the acceleration due to gravity (9.8 m/s^2). Solving for t, we get: t = sqrt(2h/g). Plugging in the values, we have: t = sqrt(2 * 250 / 9.8) = 5 s. Since the ball falls vertically, its vertical final velocity is equal to the acceleration due to gravity, which is 9.8 m/s.

To find the horizontal displacement, we can use the equation: d = v*t, where v is the horizontal velocity (40 m/s) and t is the time (5 s). Plugging in the values, we have: d = 40 * 5 = 200 m.

The vertical time is already given as 5 s. The horizontal time is also 5 s, since there is no vertical acceleration to affect the horizontal motion of the ball.

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