Suppose that you throw a rock into the air from the top of a cliff. The initial
upward velocity is 15 m/sec.
a. How high will the rock be above the cliff after two seconds?
b. Where will it be after four seconds ?
c. When will it again be at the same level you threw it?
d. When will it hit the water, 50 meters below the cliff?
Answers
Answer:
a. 10.4m above the cliff
b. 18.4m below the cliff
c. Os or 3.1s
d. 5.1s
a) The rock be 10 m above the cliff after two seconds.
b) The rock be 20 m below the cliff after 4 seconds.
c) After 3 second it again be at the same level you threw it.
d) After 5 second it hit the water, 50 m below the cliff.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, The formula for the distance,
s = ut - 1/2 gt²
Where, s is distance of an object.
u is initial velocity.
t is time taken by object.
Now,
a) Given that;
t = 2 seconds , u = 15 m/sec , g = 10 m/s
Since, s = ut - 1/2 gt²
Substitute all values we get;
s = 15 × 2 - 1/2 × 10 × 2²
s = 30 - 20
s = 10 m
Thus, The rock be 10 m above the cliff after two seconds.
b) Given that;
t = 4 second,
Then, s = ut - 1/2 gt²
s = 15 × 4 - 1/2 × 10 × 4²
s = 60 - 80
s = - 20
Hence, The rock be 20 m below the cliff after 4 seconds.
c) Given that;
s = 0 meter
Then, s = ut - 1/2 gt²
Substitute all the values,
0 = 15t - 1/2 × 10 × t²
15t - 5t² = 0
5t² - 15t = 0
5t ( t - 3) = 0
Gives, t = 0 second and t = 3second
So, After 3 second it again be at the same level you threw it.
d) Given that;
s = -50 m
Since, s = ut - 1/2 gt²
Thus, Substitute all the values we get,
- 50 = 15t - 1/2 × 10 × t²
15t - 5t² = -50
5t² - 15t - 50 = 0
5 (t² - 3t - 10) = 0
t² - 3t - 10 = 0
By using quadratic formula;
t = -(-3) ± √(-3)² - 4 × 1 × -10 / 2 × 1
t = 3 ± √9 + 40 / 2
t = 3 ± √49 / 2
t = 3 ± 7 / 2
Gives t = 3 + 7 / 2 = 5 second
and , t = 3 - 7/ 2 = -4/2 = -2 second
Thus, After 5 second it hit the water, 50 m below the cliff.
So,
a) The rock be 10 m above the cliff after two seconds.
b) The rock be 20 m below the cliff after 4 seconds.
c) After 3 second it again be at the same level you threw it.
d) After 5 second it hit the water, 50 m below the cliff.
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The equivalent fractions of the given fraction [tex]\dfrac{2}{6}[/tex] are [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex] .
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Answer:
Step-by-step explanation:
wow, this is kinda complicated math for HS.. :? we have to know what type of series this is, and that means knowing all the different kinds.. unless maybe in the instructions it tells you you are working with arithmetic series? It is one of those so we can use those formulas... other series can have much more complex formulas.. series comes up in Calc II in college.. but .. unless you're going to be an engineer you probably don't need it.. soooooo anyway..
we can use Sn = n/2(2a1 + d(n-1) )
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sounds hard huh.. :? let's see
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n = 11
The number of the terms of the sequence will be equal to 11.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Given series is 4+7+10+..... and the sum of the terms of the series is 209.
The summation of the n terms of the series is written by the formula below,
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Substitute the values in the equation above,
209 = n / 2 [(2 x 4 + ( n -1)3]
418 = n(5+3n)
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