G A3.3 - Arc Problems
Get the assessment: FA03.3.pdf
This assessment covers the following video flips:
3H. Solve Problems where an object is launched into the air at an angle.
3I. Use the range equation
The Assessment Solved:
Show your work and circle your answers to receive full credit (but don't round until the end) Ignore air friction, use the convention that down is negative, and use g = 9.80 m/s/s.
1-3. A ball is launched at 27.2 m/s at an angle of 75.0o above horizontal on a level field.
1. What time is the ball in the air?
(5.36 s)
2. What horizontal distance does it travel before hitting the ground again?
(37.7 m)
3. What is the greatest height the ball reaches? What is its speed at this height?
(35.2 m, 7.04 m/s)
4. Use the range equation to find these ranges for the velocities and launch angles:
Velocity = 34.0 m/s, Launch Angle = 43.0o Range = ?
(118 m)
Velocity = 15.0 m/s, Launch Angle = 17.0o Range = ?
(12.8 m)
5. Use the range equation to find the proper launch angles for the following velocities and ranges:
Velocity = 34.0 m/s, Range = 100. m, Launch Angles = ? and ? degrees
(29.0o and 61.0o)
Velocity = 12.0 m/s, Range = 5.00 m, Launch Angles = ? and ? degrees
(9.9o and 80.1o)
Help with the Quizlette:
Red Elk shoots an air rocket at a speed of 25.0 m/s at an angle of 57.0o above the horizontal on a very level field.
A) Break the velocity vector into components. (These become your initial velocities for x and y) Set up your horizontal/vertical table, fill it with known quantities, and solve for everything you don’t know. (You know horizontally: both velocities and the acceleration, and vertically: the displacement, both velocities, and the acceleration) (13.616 m/s x + 20.967 m/s y)
B) What are the initial horizontal and vertical velocity components? (13.616 m/s x + 20.967 m/s y)
C) What time is the rocket in the air? (4.27 s)
D) How far does the rocket go before hitting the ground? (58.2 m)
E) What is the greatest height the rocket reaches? (22.4 m)
F) What is the speed of the rocket at the highest point? (13.6 m/s)
Red Elk kicks a ball at a speed of 28.0 m/s at an angle of 34.0o above the horizontal on a very level field.
1. What time is the ball in the air? (3.20 s)
2. What horizontal distance does it travel before hitting the ground again? (74.2 m)
3. What is the greatest height the ball reaches? What is its speed at this height? (12.5 m, 23.2 m/s)
Use the range equation to find these ranges for the velocities and launch angles. Write down what you put into your calculator:
Velocity = 32.0 m/s, Launch Angle = 47.0o Range =
(104 m)
Velocity = 11.0 m/s, Launch Angle = 26.0o Range =
(9.73 m)
Use the range equation to find the proper launch angles for the following velocities and ranges. Write down what you put into your calculator:
Velocity = 29.0 m/s, Range = 32.0 m, Launch Angles = and degrees
(10.9o and 79.1o)
Velocity = 12.0 m/s, Range = 14.5 m, Launch Angles = and degrees
(40.3o and 49.7o)
Another Example:
