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Classical Mechanics

# Projectile motion - intermediate

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.

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.

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 $$g= 10 \text{ m/s}^2.$$

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 $$g =10 \text{ m/s}^2.$$

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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