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A \( 300 \text{ g} \) football is kicked with an initial velocity of \( 140 \text{ m/s} \) in a direction that makes a \( 30^\circ \) angle with the horizon. Find the peak height of the football.

Gravitational acceleration is \( g = 10 \text{ m/s}^2, \) and air resistance is negligible.

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The figure above depicts a cannon on the edge of a \( H= 73 \text{ m} \) high cliff. The cannon fires a cannonball at a \( 53 ^\circ \) angle with the horizon at a speed of \( 25 \text{ m/s} .\) If the height of the cannon itself is negligible, what is the maximum height from the ground that the cannonball reaches?

The gravitational acceleration is \( g = 10 \text{ m/s}^2, \) and \( \sin{53^\circ}\) and \(\cos{53^\circ}\) are about \(0.8\) and \(0.6,\) respectively.

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A projectile fired from the ground has a maximum range of \( 132 \text{ m}. \) What is the maximum height attained by it?

Assume that air resistance is negligible and gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

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A man kicks a \( 300 \text{ g} \) ball from the ground in a direction that makes a \(45^\circ \) angle with the horizon. He intends to make the ball land on top of a moving truck. If the initial horizontal distance between the truck and the ball, at the instant of the kick, is \(d_o = 36 \text{ m}, \) and the truck moves directly away from the ball with a velocity of \( v = 9 \sqrt{2} \text{ m/s}, \) in what magnitude of velocity \(v_o \) should the ball be kicked in order to make it land on the truck?

The height of the truck and air resistance are both negligible, and the gravitational acceleration is \( g =10 \text{ m/s}^2. \)

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Two identical marbles \(A\) and \(B\) are thrown vertically from the ground with speeds of \( 2 \text{ m/s} \) and \( 1 \text{ m/s}, \) respectively, as shown above. Let \(a\) be the distance traveled by \(A\) until it returns back to the ground. Let \(b\) be the distance traveled by \(B\) until it returns back to the ground. What is \(\displaystyle{\frac{a}{b}?}\)

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