**Practice Problems: Projectiles**Click here to see the solutions.

1. (easy) a) Study the image below from the 2016 Rio Olympics. Compare and contrast the four trajectories shown.

b) If the water spouts in the picture below shot the water at a slightly higher angle, would the landing place be closer to or further from the spouts? Assume Δy = 0.

2. (easy) Rank the range of the following projectiles:

Projectile A: Firing angle = 30°, initial speed = 40 m/s

Projectile B: Firing angle = 45°, initial speed = 40 m/s

Projectile C: Firing angle = 15°, initial speed = 40 m/s

Projectile D: Firing angle = 60°, initial speed = 40 m/s

3. (moderate) A cannonball (placed on a wall 20 m above the ground) is shot at 20° firing angle with a initial speed of 17 m/s. Determine the time it takes for the cannonball to hit the ground and the distance from the base of the wall where the projectile lands. Additionally, if one assumes that the initial speed remained the same for all firing angles, what is the maximum horizontal distance the cannonball can travel before it lands.

4. (moderate) A home run is hit in such a way as the baseball just clears a wall (21.0 m tall) located 130.0 m from home plate. The ball is hit at a 35° angle. Assume that the ball is hit 1.0 m above the ground initially. Find...

a) The initial speed of the ball

b) The time it takes to reach the wall

c) The velocity components and the speed of the ball when it reaches the wall.

5. (moderate) A projectile is launched at a 35° angle from a height of 3300 m off the ground. It lands on the ground 9400 m (in the x-direction) from the base of the launch site. Find the initial speed and the maximum height.

6. (moderate) A tennis player hits a ball with an initial speed of 23.6 m/s perfectly horizontally. The ball is 2.37 m above the ground when struck by the racquet. If the net is 12.0 m from the ball (in the x-direction), and the net height is 0.90 m, by how much does the ball clear the net?

7. (moderate) A rock is tossed at a 42°angle at an initial height of 1.2 m from the ground. 1.6 seconds after release, the rock reaches its maximum height. Find the initial velocity, the maximum height and the overall velocity at maximum height.

8. (hard) Two objects are launched from the same position, with the same initial speeds, but at different angles. The projectile fired at the lower angle bounces (upon hitting the ground) losing some of its energy while following the black trajectories. The other projectile follows the red trajectory. Find the angle θ in the sketch below.

9. (moderate) A kicker on the football team gives the ball an initial velocity of 22.0 m/s. The kick begins 40.0 m in front of the goal posts. The goal post crossbar is 3.44 m above the ground. Determine the minimum and the maximum kicking angles which will result in a field goal. Clue: It might be useful for you to remember the trig identity, 1/(cos^{2}θ) = 1 + tan^{2}θ , as a way to simplify your analysis. Use your algebraic skills to treat the term tanθ as the unknown in a quadratic equation.

10. (moderate) In every projectile example thus far, we have assumed free-fall conditions (no air resistance). Describe what you think the effect of air resistance would be on the range of a projectile. Additionally, use your ideas to predict if a projectile with an extremely big max height (very large initial speed) would have a larger range if shot at 45° or at 50°. Assume that the atmospheric density decreases with elevation.

**Please supplement these problems with those found in your companion text.**