Astone fell from the top of a cliff into the ocean.
in the air, it had an average speed of 16 m/s. in the water, it had an average speed of 3 m/s, before hitting the seabed. the total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
how long did the stone fall in the air and how long did it fall in the water?

Time the stone fall in the air = 7 seconds

Time it fall in the water = 5 seconds

Step-by-step explanation:

Given in the question,

speed of stone in the air = 16 m/s

speed of stone in the water = 3m/s

The total distance from the top of the cliff to the seabed = 127 m

the total time it took to hit the seabed = 12 s

Suppose time took to hit the water = x

so the time took from top of water to seabed = 12 - x

Formula to use

127 = 16x +  3(12-x)

127 = 16x + 36 - 3x

127 - 36 = 16x - 3x

91 = 13x

x = 91/13

x = 7 seconds

12 - x = 12 - 7 = 5 seconds

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

-232

step-by-step explanation: