1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kaheart [24]
3 years ago
6

A stone is thrown vertically upward with a speed of 15.5 m/s from the edge of a cliff 75.0 m high .

Physics
2 answers:
rjkz [21]3 years ago
5 0

a) 2.64 s

We can solve this part of the problem by using the following SUVAT equation:

s=ut+\frac{1}{2}at^2

where

s is the displacement of the stone

u is the initial velocity

t is the time

a is the acceleration

We must be careful to the signs of s, u and a. Taking upward as positive direction, we have:

- s (displacement) negative, since it is downward: so s = -75.0 m

- u (initial velocity) positive, since it is upward: +15.5 m/s

- a (acceleration) negative, since it is downward: so a= g = -9.8 m/s^2 (acceleration of gravity)

Substituting into the equation,

-75.0 = 15.5 t -4.9t^2\\4.9t^2-15.5t-75.0 = 0

Solving the equation, we have two solutions: t = -5.80 s and t = 2.84 s. Since the negative solution has no physical meaning, the stone reaches the bottom of the cliff 2.64 s later.

b) 10.4 m/s

The speed of the stone when it reaches the bottom of the cliff can be calculated by using the equation:

v=u+at

where again, we must be careful to the signs of the various quantities:

- u (initial velocity) positive, since it is upward: +15.5 m/s

- a (acceleration) negative, since it is downward: so a = g = -9.8 m/s^2

Substituting t = 2.64 s, we find the final velocity of the stone:

v = 15.5 +(-9.8)(2.64)=-10.4 m/s

where the negative sign means that the velocity is downward: so the speed is 10.4 m/s.

c) 4.11 s

In this case, we can use again the equation:

s=ut+\frac{1}{2}at^2

where

s is the displacement of the package

u is the initial velocity

t is the time

a is the acceleration

We have:

s = -105 m (vertical displacement of the package, downward so negative)

u = +5.40 m/s (initial velocity of the package, which is the same as the helicopter, upward so positive)

a = g = -9.8 m/s^2

Substituting into the equation,

-105 = 5.40 t -4.9t^2\\4.9t^2 -5.40 t-105=0

Which gives two solutions: t = -5.21 s and t = 4.11 s. Again, we discard the first solution since it is negative, so the package reaches the ground after

t = 4.11 seconds.

dimulka [17.4K]3 years ago
4 0

Answer:

(a) 5.8s

(b) 41.36m/s

(c) 99.52m

    5.21s

Explanation:

(a) This is the total time it takes the stone to reach its maximum height above the cliff and strike the ground at the base of the cliff after projection.

let the height attained by the stone above the cliff be h_1 and the time taken to attain this height be t_1. We can safely assume acceleration due to gravity to be taken as g=9.8m/s^2.

We use the first equation of motion under free fall to obtain t_1 as follows;

v=u-gt_1............(1)

given: u = 15.5m/s

Where v is the final velocity and u is the initial velocity. The negative sign in the equation indicates the fact that the stone is moving upwards against gravitational pull. The final velocity v=0 at height h_1 because the stone will momentarily at the maximum height come to rest before it begins to fall back downwards.

Hence from equation (1) we obtain the following,

0=15.5-9.8t_1\\9.8t_1=15.5\\hence\\t_1=15.5/9.8\\t_1=1.58s

To get h_1 we use the third equation as follows;

v^2=u^2-2gh_1 ( the body is moving upward so g is negative)

0^2=15.5^2-2*9.8*h_1\\0=240.25-19.6h_1\\19.6h_1=240.25\\therefore\\h_1=240.25/19.6\\h_1=12.26m

Next we obtain the time it takes to fall back from the maximum height downwards to the base of the cliff. Let this time be t_2. We use the second equation of motion.

H=ut+gt_2^2/2............(2)

( g is positive because the stone is falling downwards)

However in this case, u = 0 because the stone is falling freely from rest downwards.

H=h_1+75m=12.26+75\\H=87.26m\\

Substituting into equation (2), we obtain;

87.26=(0*t_2)+9.8t_2^2/2

Simplifying further we obtain;

4.9t_2^2=87.26\\t_2^2=87.26/4.9\\     =17.81\\t_2=\sqrt{17.81}=4.22s

Hence the total time spent in air = 1.58+4.22 = 5.8s

(b) We use the third equation of motion to find the velocity with which the stone strikes the ground.

v^2=u^2+2gH....... (3)

the stone is falling downwards in this case from height H from rest, u = 0, v is the final velocity with which is strikes the ground. Equation (3) can therefore be reduced to the following form by putting u = 0;

v=\sqrt{2gH}\\v=\sqrt{2*9.8*87.26} \\v=41.36m/s

(c) The total distance travelled is given as follows;

H_{total}=h_1+H\\H_{total}=12.26+87.26=99.52m

When the package was dropped from the ascending helicopter, it will be projected upwards with an initial velocity equal to that of the helicopter, attain a maximum height and then fall back downwards. The total time spent in air by the package is the sum of the time it takes to attain maximum height and the time it takes to fall to the ground from the maximum height. This solution is similar to that of part (a) of this question.

To find the time it takes to attain maximum height, we use equation (1): v = 0, u = 5.4m/s and g is negative since the package is moving upward against gravity. Hence;

0^2=5.4^2+9.8t_1\\9.8t_1=5.4\\t_1=5.4/9.8\\t_1=0.55s

Similarly to the previous solution, we obtain the maximum height as follows;

v^2=u^2-2gh_1\\0^2=5.4^2-2*9.8*h_1\\19.6h_1=29.16\\h_1=29.16/19.6\\h_1=1.49m

therefore maximum height is

H = 105+1.49 = 106.49m

The time taken by the package to fall from H to the ground is given by equation (2), where u = 0 since the package is falling from rest; g is positive in this case.

106.49=(0*t)+ 9.8t^2/2\\106.49=4.9t^2\\t^2=106.49/4.9=21.73\\t=\sqrt{21.73}=4.66s

therefore the total time spent by the package before striking the ground is given by;

t_{total}=0.55s+4.66s=5.21s

You might be interested in
A wave With wavelength 20 m has a frequency of 12 Hz what is the waves speed
pentagon [3]

Answer:

240m/s

Explanation:

The equation to calculate is wavelength= velocity/ frequency so to find the velocity you would have to multiply frequency by wavelength.

7 0
3 years ago
How can humans activities affect the frequency and impact of natural disasters
denpristay [2]
Forest fires can be an impact 

8 0
3 years ago
Read 2 more answers
PLEASE NEED AN ANSWER SO I CAN SUBMIT IT!!! THANK YOU IN ADVANCE (will give brainliest)
alexandr402 [8]

Answer:

Im only 12 and i need the points so ima try my best.

Explanation:

574.780616 m6 kg3 s-6 K-3 mol-3

6 0
3 years ago
An ice cube sitting on a piece of wood would melt:
Aleksandr [31]
The answer would be slowly
3 0
3 years ago
Read 2 more answers
Which of the following is NOT an important factor in selecting a medical professional?
lara31 [8.8K]

Answer:

D

Explanation:

appearance is not a imp factor . location could be imp. becoz a proper environment is need to study such courses.

5 0
3 years ago
Other questions:
  • A stunt man jumps from the top of a building and lands 10 meters below his initial height. In case A, the stunt man lands on a s
    10·1 answer
  • A simple pendulum on the surface of Earth is found to undergo 15.0 complete small‑amplitude oscillations in 8.75 s. Find the pen
    8·1 answer
  • Two spheres A and B of negligible dimensions and masses 1 kg and √3 kg respectively, are supported on the smooth circular surfac
    9·1 answer
  • A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density th
    11·1 answer
  • You set out to design a car that uses the energy stored in a flywheel consisting of a uniform 101-kg cylinder of radius r that h
    6·1 answer
  • 2.
    10·1 answer
  • There is fluctuation in time measured by a pendulum clock why give reasons​
    14·1 answer
  • Tips to get friends?
    10·1 answer
  • A mercury manometer is connected to a container of gas. (a) The height of the mercury column on the side connected to the gas is
    6·1 answer
  • how long will it take the bird to cover a ground distance of 550 km from north to south? (note that even on cloudy nights, many
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!