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
What is the difference between speed and velocity?
mixer [17]
  • Speed is the rate of change of distance with time while velocity is the rate of change of displacement with time.
  • Speed is a scalar quantity while velocity is a vector quantity.
  • Speed cannot be negative but velocity can be negative.

Hope you could get an idea from here.

Doubt clarification - use comment section.

8 0
2 years ago
A ball is projected horizontally from the top of a hill with a velocity of 30m/s if it reaches the ground 5sec later the height
Vikki [24]

Answer:

The hill is a total of 150 meters tall

Explanation:

30×5=150

7 0
2 years ago
When vibrational motion in an object increases, which is a true statement?
ss7ja [257]
Hello friend!!

We know that kinetic energy is the energy possessed due to the motion of the object. And we know if the object is in a fast motion then the temperature would be high, whereas if the object is slow in motion then it will have lower temperature. So we know that the kinetic energy is indirectly related to temperature.From our knowledge we can conclude that HIGHER THE TEMPERATURE, HIGHER THE KINETIC ENERGY and LOWER THE TEMPERATURE, LOWER THE KINETIC ENERGY.
Hence, the answer to your question here is,a.kinetic energy, temperature, and thermal energy increase. 
Hope it helps!!All the best!!
5 0
3 years ago
How to tell if a circuit is connected in.a series.or parallel?
stepladder [879]

Series circuits split the voltage of resistors, so if you see several diodes connected <em>in series </em>or all next to each other, just a complete loop, it will be in series.

Parallel circuits split the current of resistors, so if you see several diodes connected along different branches or pathways, it will be in parallel.

7 0
3 years ago
In a two-body collision, if the momentum of the system is conserved, then which of the
lakkis [162]

Answer:

c) may also be conserved

Explanation:

Momentum is conserved  in both elastic and inelastic type of collisions.

But the differences is that:

In an ELASTIC type of collisions, KINETIC ENERGY IS ALSO CONSERVED.

whereas, In an INELASTIC type of collision, KINETIC ENERGY IS NOT CONSERVED.

So unless until type of collision is specified, we can not say anything about the conservation of kinetic energy after collision.

Hence, may also be conserved is the appropriate option here.

5 0
2 years ago
Other questions:
  • Five race cars speed toward the finish line at the Jasper County Speedway. The table lists each car’s speed in meters/second. If
    9·2 answers
  • What happens to the frequency of a wave if its energy increases?
    14·2 answers
  • What three basic components are atoms made of?
    12·1 answer
  • Help please...
    9·1 answer
  • In what medium would light have the longest wavelength
    10·1 answer
  • A child bounces a 52 g superball on the sidewalk. The velocity change of the superball is from 20 m/s downward to 14 m/s upward.
    8·2 answers
  • A spherical steel ball bearing has a diameter of 2.540 cm at 26.00°C. (Assume the coefficient of linear expansion for steel is 1
    12·1 answer
  • A particle decelerates uniformly from a speed of 30 cm/s to rest in a time interval of 5.0 s. It then has a uniform acceleration
    10·1 answer
  • What will the skydivers ke be when he land on the groun
    7·1 answer
  • According to relativity theory, if a space trip finds a son or daughter biologically older than his or her parents, then the spa
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!