Basic Concepts
This is the path that a projectile follows through the air.
What is a parabola (or trajectory)?
A diver runs horizontally off the end of a diving board with an initial speed of 1.75 m/s. If the diving board is 3.00 m above the water, (a) how far away from the diving board does the diver enter the water, and (b) with what speed does the diver enter the water?
1.37 m, 7.87 m/s
A basketball player shooting a free throw demonstrates this type of motion.
What is projectile motion?
If you drop a ball and throw another horizontally at the same time from the same height, this one hits the ground first.
What is neither (they hit at the same time)?
This is what happens to the vertical velocity of a projectile throughout its flight (ignoring air resistance).
What is it consistently changes?
These are the two components of projectile motion that are analyzed independently.
What are horizontal and vertical motion?
A placekicker kicks a football at an angle of 40.0º above the horizontal. The initial speed of the ball is 22 m/s. Ignore air resistance and find the maximum height that the ball attains. Determine the time of flight between kickoff and landing. Calculate the range of the projectile.
10 m, 2.9 s, 49 m
At this angle, a ball shot with the same initial velocity will land in the same spot as a ball launched at 30 degrees.
What is 60 degrees?
This component of velocity remains constant.
What is the horizontal velocity component (vx)?
The velocity vector of a projectile is always broken up into this.
What are the vertical and horizontal components?
This force is the only force acting on a projectile after it leaves the launching point (ignoring air resistance).
What is gravity?
A ball is thrown horizontally from the top of a building 35 m high. The ball strikes the ground at a point 80 m from the base of the building. Find (a) the time the ball is in flight, (b) its initial velocity, and (c) the velocity just before the ball strikes the ground.
2.67 s, 29.9 m/s, 39.8 m/s, -41.2˚
A football punter kicks the ball at this optimal angle to achieve maximum distance.
What is 45 degrees?
If it takes t seconds for a projectile to reach its max height, the total time of flight is this.
What is 2t?
At the peak of its trajectory, a projectile has only this type of velocity.
What is horizontal velocity?
At the highest point of a projectile's path, this velocity component equals zero.
What is vertical velocity (vᵧ)?
A place kicker must kick a football from a point 36.0 m (about 40 yards) from the goal and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0˚ to the horizontal. By how much does the ball clear or fall short of clearing the crossbar?
clears by 0.89 m
Water from a garden hose follows this type of curved path due to gravity.
What is a parabolic trajectory?
This is the only thing that can increase or decrease the time it takes for a projectile to hit the ground when starting from a consistent height.
What is v0y?
This is the relationship between launch angle and landing angle for a projectile that lands at the same height it was launched.
What is they are equal (symmetric)?
This is the angle that produces maximum range for a projectile launched from ground level.
What is 45 degrees?
If a projectile has a launching angle of 52.0º above the horizontal and an initial speed of 18.0 m/s, what is the highest barrier that the projectile can clear?
10.3 m
If I had the vertical and horizontal components of velocity, this is the equation I would use to find the total velocity.
What is the pythagorean theorem, or vx2+vy2=v2?
A ball dropped from a moving car will follow this type of path as observed by someone in the car.
What is a linear path (or it falls straight down)?
When air resistance is considered, the actual range of a projectile is this compared to the theoretical range.
What is less than (or shorter)?