Parameterics Review Day 1 – 3
1. Matt wants to cross a river which is 0.5 miles wide on his kayak. However, today there
is a 5 mi/hr current. When he reaches the opposite shore, he finds that he has landed at
a point ¾ of a mile down stream.
Model the path of Matt’s boat with parametric equations.
How far did Matt actually travel?
How long did it take him?
What was Matt’s actual speed?
What was the angle of the actual path, relative to her intended path straight across the
river?
2. A.J. is eating spaghetti and a meat ball rolls off his plate with a horizontal
velocity of 3 ft/sec . The table is 4 ft high.
Model the path of the ball using parametric equations.
How long does it take for the meatball to hit the floor?
How far from the table does the meatball hit the floor?
3. You hit a soccer ball from the ground at an angle of 320 at a rate of 30 ft/sec.
a) When will the ball hit the ground?
b) How far does the ball travel in the horizontal direction?
c) What time will the ball be at the maximum height?
d) What is the maximum height attained by the ball?
4. Val hits a baseball with an initial speed of 100 feet per second at an angle of 40o to the
horizontal. The ball was hit at a height of 3.5 feet off the ground.
Find equations to describe the position of the ball as a function of time.
How long is the ball in the air?
Determine the distance the ball travels.
When is the ball at its maximum height? Determine the maximum height.
Will the ball clear a 7 foot fence if the fence is 130 feet away?
There is a 10 feet per second wind blowing in horizontally against the path of the ball.
Will the ball clear a 7 foot fence if the fence is 130 feet away?
Parameterics Review Day 1 – 3
1. Matt wants to cross a river which is ____ miles wide on his kayak. However, today
there is a _____ mi/hr current. When he reaches the opposite shore, he finds that he
has landed at a point ¾ of a mile down stream.
Model the path of Matt’s boat with parametric equations.
How far did Matt actually travel?
How long did it take him?
What was Matt’s actual speed?
What was the angle of the actual path, relative to her intended path straight across the
river?
2. A.J. is eating spaghetti and a meat ball rolls off his plate with a horizontal
velocity of ______ ft/sec . The table is 4 ft high.
Model the path of the ball using parametric equations.
How long does it take for the meatball to hit the floor?
How far from the table does the meatball hit the floor?
3. You hit a soccer ball from the ground at an angle of ______ at a rate of _____ ft/sec.
a) When will the ball hit the ground?
b) How far does the ball travel in the horizontal direction?
c) What time will the ball be at the maximum height?
d) What is the maximum height attained by the ball?
4. Val hits a baseball with an initial speed of ______ feet per second at an angle of 40o to
the horizontal. The ball was hit at a height of 3.5 feet off the ground.
Find equations to describe the position of the ball as a function of time.
How long is the ball in the air?
Determine the distance the ball travels.
When is the ball at its maximum height? Determine the maximum height.
Will the ball clear a 7 foot fence if the fence is 130 feet away?
There is a 10 feet per second wind blowing in horizontally against the path of the ball.
Will the ball clear a 7 foot fence if the fence is 130 feet away?
Review HW days 1 - 3
1. Emma wants to fly to a town which lies 300 miles directly to the east. Her plane can fly at 150
mph. She ignores the wind and heads directly east. However, there is a 30 mph wind blowing from
the north which sends her plane off track.
a)Model the path of the plane using parametric equations.
b) How far off course is the plane?
c) How far has the plane actually traveled?
d) What was the plane’s actual speed?
2. A pen is rolled off the end of a table with a horizontal velocity of 1.1 ft/sec.
The table is 4 ft high.
a) Model the path of the pen using parametric equations
b) How long does it take for the ball to hit the floor?
c) How far from the table does the ball hit the floor?
3. You are standing on a beach and you kick a rock into a lake at an angle of 520 at a rate
of 40 ft/sec.
a) When will the rock hit the lake?
b) How far does the rock travel in the horizontal direction?
c) What time will the rock be at the maximum height?
d) What is the maximum height attained by the rock?
4. Mickey Mantle hits a ball with an initial velocity of 103 feet/sec at an angle of 620 from a height
of 3 feet.
a.) Find equations to describe the position of the ball as a function of time.
b.) How long is the ball in the air?
c.) Determine the distance the ball travels.
d.) When is the ball at its maximum height? Determine the maximum height.
e.) Will the ball clear a 10 foot fence if the fence is 380 feet away?
f.) There is a 7 feet per second wind blowing in horizontally with the path of the ball.
Will the ball clear a 10 foot fence if the fence is 380 feet away?