Classical Mechanics

2D Kinematics

Projectile motion - intermediate

         

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

Gravitational acceleration is g=10 m/s2, g = 10 \text{ m/s}^2, and air resistance is negligible.

The figure above depicts a cannon on the edge of a H=73 m H= 73 \text{ m} high cliff. The cannon fires a cannonball at a 53 53 ^\circ angle with the horizon at a speed of 25 m/s. 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 m/s2, g = 10 \text{ m/s}^2, and sin53 \sin{53^\circ} and cos53\cos{53^\circ} are about 0.80.8 and 0.6,0.6, respectively.

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

Assume that air resistance is negligible and gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2.

A man kicks a 300 g 300 \text{ g} ball from the ground in a direction that makes a 4545^\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 do=36 m,d_o = 36 \text{ m}, and the truck moves directly away from the ball with a velocity of v=92 m/s, v = 9 \sqrt{2} \text{ m/s}, in what magnitude of velocity vov_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 m/s2. g =10 \text{ m/s}^2.

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

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