How to solve problems on projectiles launched at an angle

This is a detailed tutorial on how to solve problems involving projectiles launched at an angle, where the start and end points are not of the same height.

Related playlist:    • Projectile Motion  

Timestamps:

00:00 – learning target
0:28 – problem overview and overview of problem-solving steps
1:14 – solving for the vertical displacement of a projectile
13:00 – solving for the final vertical velocity of a projectile
15:55 – solving for the horizontal displacement of a projectile (uses quadratic equation/formula)

Copy of the problems solved:

1. In a carnival booth, you can win a stuffed toy by tossing a coin into a small dish. The dish is placed on a shelf above the point where the coin leaves your hand, with a horizontal distance of 2.5 m from that point. If you throw the coin with a velocity of 6.0 m/s at an angle of 62° above the horizontal, it will land in the dish. Ignore air resistance.
a. How high is the shelf above the point where the coin leaves your hand?
b. What is the vertical component of the coin’s velocity just before it lands in the dish?

2. You throw a ball from your window 8.0 m above the ground. The ball leaves your hand at a velocity of 10.0 m/s at an angle of 20° below the horizontal. At what horizontal distance from your window will the ball hit the ground? Ignore air resistance.