Example John throws the ball straight upward and after 1 ...



TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES

363 P. Casal St., Quiapo, Manila

FREELY FALLING BODIES

A Compilation of Problems with Solutions in

Calculus-Based Physics I

Prepared for:

Engr. Eleazar Lagman

Prepared by:

Al Clinton M. Soriano

Abdul Jaber Cabuntalan

Arsenio M. Tuazon III

Section:

Schedule:

1. John throws the ball straight upward and after 1 second it reaches its maximum height then it does free fall motion which takes 2 seconds. Calculate the maximum height and velocity of the ball before it crashes the ground. (g=10m/s²)

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2. An object does a free fall motion. It hits the ground after 4 seconds. Calculate the velocity of the object after 3 seconds and before it hits the ground. What can be the height it is thrown?

[pic]



3. Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

|Diagram: |Given: |Find: |

|[pic] |vi = 0.0 m/s |t = ?? |

| |d = -8.52 m | |

| | | |

| |a = - 9.8 m/s2 | |

[pic]

-8.52 m = (0 m/s)*(t) + 0.5*(-9.8 m/s2)*(t)2

-8.52 m = (0 m) *(t) + (-4.9 m/s2)*(t)2

-8.52 m = (-4.9 m/s2)*(t)2

(-8.52 m)/(-4.9 m/s2) = t2

1.739 s2 = t2

t = 1.32 s

4. Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.

|Diagram: |Given: |Find: |

|[pic] |vi = 26.2 m/s |d = ?? |

| |vf = 0 m/s | |

| | | |

| |a = -9.8 m/s2 | |

[pic]

(0 m/s)2 = (26.2 m/s)2 + 2*(-9.8m/s2)*d

0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2)*d

(-19.6 m/s2)*d = 0 m2/s2 -686.44 m2/s2

(-19.6 m/s2)*d = -686.44 m2/s2

d = (-686.44 m2/s2)/ (-19.6 m/s2)

d = 35.0 m



5. How long does it take a ball to reach the ground 7.0 m below, if it is thrown straight up with an initial speed of 2.00 m/s?

d = vit + (0.5)at2

(7.0 m) = (-2.00)t + (0.5)(9.8)t2

t = {1.42, -1.01}

Since t < 0 has no meaning,

t = 1.42 s

6.  A ball is dropped from a roof to the ground 8.0 m below. A rock is thrown down from the roof 0.600 s later. If they both hit the ground at the same time, what was the initial speed of the rock?

|  |ball |rock |

|d |8.0 m [down] |8.0 m [down] |

|a |9.8 m/s2 [down] |9.8 m/s2 [down] |

|vf |  |  |

|vi |0 |? |

|t |? |? |

 

We need time to find speed. Since we have more information about the ball we start off solving for time for the ball. Now we can see we need a relationship between d, a, vi, and t

d = vit + (0.5)at2

8.0 = (0)t + (0.5)(9.8 m/s2)t2

t = 1.28 s

The time of travel for the rock is 0.600 s less than for the ball. Now our table looks like this:

|  |ball |rock |

|d |8.0 m [down] |8.0 m [down] |

|a |9.8 m/s2 [down] |9.8 m/s2 [down] |

|vf |  |  |

|vi |0 |? |

|t |1.28 s |0.68 s |

For the rock we need a relationship between d, a, vi, and t

d = vit + (0.5)at2 

8.0 = vi(0.68 s) + (0.5)(9.8 m/s2)(0.68 s)2 

vi = 8.43 m/s



7. A 10 [kg] object is dropped from rest.

a. How far will it drop in 2 [s]?

[pic]

b. How long will it take a 5 [kg] object to drop the same distance?

It will take the less massive object the same amount of time (2 [s]) to fall the same distance because the acceleration due to gravity is a constant and doesn’t depend upon mass.

8. An object is dropped from rest from the top of a 100 [m] building. How long will it take for the object to hit the ground?

[pic]

9. A cliff diver from the top of a 100 [m] cliff. He begins his dive by jumping up with a velocity of 5 [m/s].

a. How long does it take for him to hit the water below?

b. What is his velocity right before he hits the water?

It is easier to solve part b of this problem prior to solving part a.

b.

[pic]

a.

. [pic]

10. Alan Iverson slam dunks a basketball and a physics student observes that Iverson’s feet are 1 [m] above the floor at his peak height. At what upward velocity must Iverson leave the floor to achieve this?

[pic]



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