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
denis-greek [22]
3 years ago
9

(a) Calculate the height (in m) of a cliff if it takes 2.48 s for a rock to hit the ground when it is thrown straight up from th

e cliff with an initial velocity of 8.19 m/s. m (b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed
Physics
1 answer:
oee [108]3 years ago
7 0

Answer:

(a) The height of the cliff is 9.92 m

(b) Time taken to reach the ground is 0.81 s

Explanation:

Given;

time of motion of the rock, t = 2.48 s

initial velocity of the rock, u = 8.19 m/s

(a) This is a two-way problem;

maximum upward height reached by the rock (h) + Total distance traveled downwards from the top (H).

Height of cliff = H - h

Maximum height reached by the rock;

v^2 = u^2 - 2gh\\\\0 = (8.19)^2 - (2\times 9.8)h\\\\0 = 67.08 - 19.6 h\\\\19.6h = 67.08\\\\h = \frac{67.08}{19.6} \\\\h = 3.422 \ m

Time to reach the maximum height;

h = ut - \frac{1}{2} gt^2\\\\3.422 = 8.19t - (0.5 \times 9.8)t^2\\\\3.422 = 8.19t - 4.9t^2\\\\4.9t^2 -8.19t + 3.422 = 0\\\\This \ forms \ a quadratic \ equation ; \\\\a = 4.9, b = -8.19, c = 3.422\\\\t = \frac{-b \ \ +/- \ \ \sqrt{b^2 -4ac} }{2a} \\\\t = \frac{-(-8.19) \ \ +/- \ \ \sqrt{(-8.19)^2 -4(4.9\times 3.422)} }{2(4.9)} \\\\t = \frac{8.19 \ \ + /- \ \ \sqrt{0.0049} }{9.8} \\\\t = \frac{8.19 - 0.07}{9.8}  \ \ or \ \ t = \frac{8.19 + 0.07}{9.8} \\\\t = 0.83 \ s \ \ or \ \ t = 0.84 \ s\\\\

The time taken for rock to falll to the gound;

t₂ = 2.48 - 0.83 s

t₂ = 1.65 s

The distance traveled downwards is calculated as

H = vt + ¹/₂gt²

where;

v is the final velocity at maximum height = initial velocity when the rock starts moving downwards = 0

H =  ¹/₂gt²

H = 0.5 x 9.8 x (1.65)²

H = 13.34 m

The height of the cliff = 13.34 m - 3.422m = 9.92 m

(b) time taken to reach the ground if thrown with the same speed;

h = ut + ¹/₂gt²

9.92 = 8.19t + (0.5 x 9.8)t²

9.92 = 8.19t + 4.9t²

4.9t² +  8.19t  - 9.92 = 0

a = 4.9,  b = 8.19,  c = -9.92

use the quadratic formula;

t = \frac{-b \ \ +/- \ \ \sqrt{b^2 -4ac} }{2a} \\\\t = \frac{-8.19 \ \ +/- \ \ \sqrt{(8.19)^2 -4(4.9\times -9.92)} }{2(4.9)} \\\\t = 0.81 \ s

You might be interested in
Which of Newton's motion laws BEST explains WHY a rock falls when it is dropped from a bridge?
erma4kov [3.2K]
It’s A because it stays in motion whenever you drop it
4 0
3 years ago
Read 2 more answers
what are the three types of solenoids, which one is the most common, and which one is used in pinball machines?​
amm1812

Answer:

The types of solenoids are: AC Laminated Solenoid , DC Solenoid , Linear Solenoid ,and Rotary Solenoid.

Explanation:

  • The main purpose of solenoid is to generate the controlled magnetic field that can be used in many forms.
  • The most common use of solenoid is done in the pinball game.
  • The Flipper solenoid that uses the two coil are used in the mechanism of pinball machines.
  • One coil of the solenoid is supplied with high electric current where as other one has the weak current flowing through it.
7 0
3 years ago
How do climate differences affect the movement at the Mariana Trench
vovangra [49]
It pushes the currents to opposite sides
8 0
3 years ago
The data table shows some data related to the Sun and the planets in our solar system.
AlexFokin [52]
You have selected the correct answer and blobbed over it with your pencil.

I assume you must have looked at Saturn's average distance, found 1427,
divided that number by 6, got 237 and change, then looked at the others,
and found that 228 was the only one that's anywhere close.
8 0
3 years ago
Read 2 more answers
How does an increase in temperature generally affect the rate of a reaction?
Zigmanuir [339]

Most reactions are exothemic. If the forward reaction of an equilibrium reaction is exothemic then the reverse reaction must be endothermic.

If a system in equilibrium is heated, it will move in exothermic direction to give out heat energy.

7 0
3 years ago
Other questions:
  • Which of the following statements are true of solids? A.The particles do not vibrate. B.The particles are in a fixed location. C
    6·1 answer
  • Newton's First Law of Motion states that an object will remain at rest or in uniform motion in a straight line unless acted upon
    14·2 answers
  • Find the intensity of a 55 dB sound given I 0=10^-12W/m^2
    6·1 answer
  • 7.22 Ignoring reflection at the air–water boundary, if the amplitude of a 1 GHz incident wave in air is 20 V/m at the water surf
    6·1 answer
  • What is the average acceleration of the particle within the time interval 1 second to 3 seconds? A. -1 meter/second2 B. 0 meters
    14·1 answer
  • Three balls are kicked from the ground level at some angles above horizontal with different initial speeds. All three balls reac
    5·1 answer
  • 1. What is the sensor that focuses and image in a camera called?
    5·2 answers
  • Plz help with this<br> And thanks
    14·2 answers
  • - A wooden crate that measures 2.0 m long and 0.40 m wide rests on
    9·1 answer
  • A bus starts from village A at 7:00 am and reaches village B at 8:30 am. If the distance between the villages A and B is 60 km.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!