# a 90 kilogram diver jumped from a cliff. if it takes 2.26 seconds for the diver to hit the water, how high is the cliff?

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## 2.7 Falling Objects – College Physics: OpenStax

## 13 2.7 FALLING OBJECTS

### Summary

Describe the effects of gravity on objects in motion.

Describe the motion of objects that are in free fall.

Calculate the position and velocity of objects in free fall.

Falling objects form an interesting class of motion problems. For example, we can estimate the depth of a vertical mine shaft by dropping a rock into it and listening for the rock to hit the bottom. By applying the kinematics developed so far to falling objects, we can examine some interesting situations and learn much about gravity in the process.

## GRAVITY

The most remarkable and unexpected fact about falling objects is that, if air resistance and friction are negligible, then in a given location all objects fall toward the center of Earth with the same constant acceleration, independent of their mass. This experimentally determined fact is unexpected, because we are so accustomed to the effects of air resistance and friction that we expect light objects to fall slower than heavy ones.

**Figure 1.**A hammer and a feather will fall with the same constant acceleration if air resistance is considered negligible. This is a general characteristic of gravity not unique to Earth, as astronaut David R. Scott demonstrated on the Moon in 1971, where the acceleration due to gravity is only

**1.67 m/s2**.

In the real world, air resistance can cause a lighter object to fall slower than a heavier object of the same size. A tennis ball will reach the ground after a hard baseball dropped at the same time. (It might be difficult to observe the difference if the height is not large.) Air resistance opposes the motion of an object through the air, while friction between objects—such as between clothes and a laundry chute or between a stone and a pool into which it is dropped—also opposes motion between them. For the ideal situations of these first few chapters, an object falling without air resistance or friction is defined to be in **free-fall**.

The force of gravity causes objects to fall toward the center of Earth. The acceleration of free-falling objects is therefore called the **acceleration due to gravity**. The acceleration due to gravity is constant, which means we can apply the kinematics equations to any falling object where air resistance and friction are negligible. This opens a broad class of interesting situations to us. The acceleration due to gravity is so important that its magnitude is given its own symbol, gg size 12{g} {}. It is constant at any given location on Earth and has the average value

g = 9.80 m/s 2 . g=9.80 m/s2. Although g g varies from 9.78 m/s 2 9.78 m/s2 to 9.83 m/s 2 9.83 m/s2

, depending on latitude, altitude, underlying geological formations, and local topography, the average value of

9.80 m/s 2 9.80 m/s2

will be used in this text unless otherwise specified. The direction of the acceleration due to gravity is downward (towards the center of Earth). In fact, its direction defines what we call vertical. Note that whether the acceleration

a a

in the kinematic equations has the value

+ g +g or − g −g

depends on how we define our coordinate system. If we define the upward direction as positive, then

a = − g = − 9.80 m/s 2 a=−g=−9.80 m/s2

, and if we define the downward direction as positive, then

a = g = 9.80 m/s 2 a=g=9.80 m/s2 .

## ONE-DIMENSIONAL MOTION INVOLVING GRAVITY

The best way to see the basic features of motion involving gravity is to start with the simplest situations and then progress toward more complex ones. So we start by considering straight up and down motion with no air resistance or friction. These assumptions mean that the velocity (if there is any) is vertical. If the object is dropped, we know the initial velocity is zero. Once the object has left contact with whatever held or threw it, the object is in free-fall. Under these circumstances, the motion is one-dimensional and has constant acceleration of magnitude

g . g.

We will also represent vertical displacement with the symbol

y y and use x x

for horizontal displacement.

### KINEMATIC EQUATIONS FOR OBJECTS IN FREE FALL WHERE ACCELERATION = -G

v = v 0 − g t v=v0−gt y = y 0 + v 0 t − y=y0+v0t− 1 2 12 g t 2 gt2 v 2 = v 2 0 − 2 g ( y − y 0 ) v2=v02−2g(y−y0)

### Example 1: Calculating Position and Velocity of a Falling Object: A Rock Thrown Upward

A person standing on the edge of a high cliff throws a rock straight up with an initial velocity of 13.0 m/s. The rock misses the edge of the cliff as it falls back to earth. Calculate the position and velocity of the rock 1.00 s, 2.00 s, and 3.00 s after it is thrown, neglecting the effects of air resistance.

Source : **pressbooks.bccampus.ca**

## A cliff diver falls from a 90 foot cliff how long will it take him to reach the water?

Answer: I would re-arrange the equation (that I remember) s = u.t +0.5.a.t^2, with acceleration due to gravity (a) in compatible units (i.e. some combination of feet and seconds), assume that initial velocity u=0, and s is the distance. This means you just need to re-arrange s = 0.5.a.t^2 and ca...

A cliff diver falls from a 90 foot cliff how long will it take him to reach the water?

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1 Answer Dave Evenden

, PhD; Engineering background; Academic researcher; PGCAP

Answered 1 year ago · Author has 71 answers and 13.9K answer views

I would re-arrange the equation (that I remember) s = u.t +0.5.a.t^2, with acceleration due to gravity (a) in compatible units (i.e. some combination of feet and seconds), assume that initial velocity u=0, and s is the distance.

This means you just need to re-arrange s = 0.5.a.t^2 and calculate time t, the units of which in this case would be seconds.

280 views Related answers Related Answer Peter Webb

Updated 6 years ago · Author has 12.2K answers and 16.7M answer views

If I jump from a 32 ft high cliff diving spot, how many feet underwater should I expect to reach?

Originally Answered: If I jump from a 32 ft high cliff diving spot, how many feet underwater should I expect to reach below fresh water level?

1. "If I jump from a 32 ft high cliff diving spot, how many feet underwater should I expect to reach below fresh water level?"

Depends on how you dive in. An expert stunt man can probably fall into 6 foot of water and not touch the bottom by turning his downward motion into horizontal. An idiot could do this by falling spreadeagled, but that would kill him. Falling vertically in straight upwards with your hands by your body, you would probably go in 6 or 7 feet plus your height ie you might need 10 - 13 feet of water. I wouldn't try it in less than 20 feet water, but I'm a coward.

2. "Is i Related Answer Urvi Kasar

, MA Psychology, Preventive and Primitive Health Care from Appollo Hyderabad, Barkatullah University, Bhopal (1…

Answered 1 year ago · Author has 4.7K answers and 1.4M answer views

What are the stresses on the body if we jump from a cliff of 20 feet to water?

Well , jumping from high to down , jumping into water from to much height , jumping into fire to save one's life or for stunts or anything courageous act like that your brain first react on that ---

Fear inside u increase your heart rate , u get sweating , nervous , body gets shaking so it depends . Over fear , over nervousness may cause heart attack too if u are forced by someone to do that for which your mind is not ready , specially when u are sensitive or have any cardiac problem or have asthma problem or any kind of medical condition. That is why in pungy jumping only healthy people who ar

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Related Answer Brad Moffat

Answered 1 year ago · Author has 2.8K answers and 5.8M answer views

A diver falls horizontally off a 20 m high cliff and strikes the water. How long does the diver take to hit the water?

A diver falls horizontally off a 20 m high cliff and strikes the water. How long does the diver take to hit the water?

There are five kinematics variables.

Simple (meaning one step) kinematics questions must always give the values of three of these five or the problem can’t be solved.

In this question it looks like you’ve only been given one, but in fact, you should realise that you have been given the displacement,

Δx Δx , the acceleration, a a

, and the initial velocity ,

v 1 v1 .

Now you can calculate the time using the most often used relationship :

Δx= v 1 Δt+ 1 2 aΔ Δx=v1Δt+12aΔ Related Answer Paul Doane

, former Propulsion Engineer, Eventually Director (1968-2008)

Answered 1 year ago · Author has 166 answers and 34K answer views

A car fails to brake and goes careening off a 20m tall cliff. If they land 48m from the cliff base, what was their initial speed? How long were they falling for?

Originally Answered: A car fails to break and goes careening off a 20m tall cliff. If they land 48m from the cliff base, what was their initial speed? How long were they falling for?

The time it takes to fall 20m is given by D = 1/2at^2. So the time t = sqrt(40m/9.81m/s^2), which is roughly 2 seconds. So the car was going 24m/sec when it left the cliff.

Related Answer Viet Nguyen

, lives in Scottsdale, AZ

Answered 3 years ago

How can I safely do a cliff jump into the water?

Originally Answered: What precautions should we take before cliff diving (jumping off cliffs into the lake)?

Make sure you have no hesitations jumping off a cliff, because if you run and stop, it’s not good. Be sure to push yourself off the cliff with your right or left feet. Definitely know the depth of where you’re jumping off from.

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Related Answer Louis M. Rappeport

, B.S. from University of California, Berkeley

Answered 2 years ago · Author has 6.8K answers and 4.2M answer views

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