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
3. A car does an emergency stop from 144 km\h in 4s<br> What was its deceleration?
strojnjashka [21]

Answer:

36?

Explanation:

5 0
2 years ago
If the total mass is m, find the moment of inertia about an axis through the center and perpendicular to the plane of the square
My name is Ann [436]
Question: A thin, uniform rod is bent into a square<span> of... A thin, uniform rod is bent into a </span>square<span> of side length a. </span>If the total mass is M<span>, </span>find the moment of inertia about an axis through the center and perpendicular to the plane of the square<span>. </span>Use the parallel-axis theorem<span>.</span>
5 0
3 years ago
Why is earth a magnet?
oksian1 [2.3K]
I hope this helps. it was right when i took the test.

7 0
3 years ago
#2 A car accelerates from rest at 4 m/s^2. What is the velocity of the car after 4 second?
solmaris [256]
You use the equation Velocity = Acceleration X Time. 4x4=16m/s.


The car travels 18m in 3 seconds.
3 0
3 years ago
Pls help will give brainlest​
Karo-lina-s [1.5K]

Respon

lqiudos ciopatmibes

ly  apsamtios ccoriendor sabe r

llpop

io.

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which statement accurately classifies helium?
    10·1 answer
  • A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the hor
    6·1 answer
  • Which statement is true of a convex lens?
    11·2 answers
  • An Earth satellite needs to have its orbit changed so the new orbit will be twice as far from the center of Earth as the origina
    7·1 answer
  • Kara Less was applying her makeup when she drove into South's busy parking lot last Friday morning. Unaware that Lisa Ford was s
    9·2 answers
  • Our brain works to create:
    8·2 answers
  • What measurement do geologists use to find absolute age
    9·2 answers
  • What causes a submarine to rise and descend?
    11·1 answer
  • Would u rather/ get ur dream car or live in a van and never pay taxes
    11·1 answer
  • How long does it for a car to cover 100 miles at 60 mi/hr? Use one of the following equations:
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!