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Calculus I - Free Fall Problems, Schemes and Mind Maps of Calculus

Solutions to problems related to free fall in calculus i. It includes four examples with different initial velocities, heights, and distances. Students will learn how to calculate maximum height, time of flight, and final velocity of objects in free fall.

What you will learn

  • How long does it take for a rock thrown downward from a cliff with an initial velocity of 50 ft/sec to reach the ground?
  • How long does it take for a ball thrown upward with an initial velocity of 80 ft/sec to reach the ground?
  • What is the maximum height reached by a rock jettisoned downward from a cliff with an initial velocity of 40 ft/sec?
  • What is the maximum height reached by a ball thrown upward with an initial velocity of 80 ft/sec?

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/27/2022

shailen_555cell
shailen_555cell 🇺🇸

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Calculus I
Section 6.6 Free Fall
1. A ball is thrown vertically upward from ground level with a velocity of 80 ft/sec.
a. When will the ball reach its maximum height?
b. What is the maximum height?
c. How long is the entire trip?
d. What is the ball’s velocity when it hits the ground?
e. What is the velocity of the ball when it is 96 ft. off the ground?
2. A rock is jettisoned with velocity 40 ft/sec from the top of a cliff that is 100 ft. high.
a. When will the rock reach its maximum height? How high will it go?
b. What is the rocks velocity when it hits the ground at the base of the cliff?
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Calculus I Section 6.6 – Free Fall

  1. A ball is thrown vertically upward from ground level with a velocity of 80 ft/sec.

a. When will the ball reach its maximum height?

b. What is the maximum height?

c. How long is the entire trip?

d. What is the ball’s velocity when it hits the ground?

e. What is the velocity of the ball when it is 96 ft. off the ground?

  1. A rock is jettisoned with velocity 40 ft/sec from the top of a cliff that is 100 ft. high.

a. When will the rock reach its maximum height? How high will it go?

b. What is the rocks velocity when it hits the ground at the base of the cliff?

Calculus I Section 6.6 – Free Fall

  1. A rock is thrown straight down with velocity 50 ft/sec. from the top of a 120 ft. cliff.

a. What is the velocity of the rock upon release?

b. How long will it take the rock to reach the base of the cliff?

c. What is the rock’s velocity at impact?

  1. A ball is thrown off the roof of a 20-foot tall house. It hits the ground 4 seconds later.

a. What was the ball’s initial velocity?

b. How high did the ball go?