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Subtitles generated by robot

00:01

hi for today's video we're going to
solve a situational problem from the
concept of projectile motion using
inverse trig function the problem is
if an object is directed in an angle
theta with theta element of closed
interval 0 to pi over 2 then the range
will be r is equals to v sub 0 squared
over g
times sine 2 theta in feet where v sub 0
in feet per second is the initial speed

00:31

and g is equals to 32 feet per second
squared is the acceleration due to
gravity
at what angle should the object be
directed so that the range will be 100
feet given that the initial speed is v
sub zero is equals to 80 feet per second
the given are as follows
r is equals to 100 feet where r
represents the range
v sub 0 is equals to 80 feet per second
where it represents the initial speed

01:02

and
g
is equals to 32 feet per second squared
which is the acceleration due to gravity
to solve for this problem let us plug in
the given values to the formula provided
to find the angle
the formula is r is equals to v sub 0
squared over g times sine 2 theta
substitute 100 to r 8 a squared to v sub
0 squared
32 to g it will be 100 is equals to 80

01:36

squared over 32 times sine 2 theta
multiply both sides by 32 over 80
squared
now let us reduce the 8 squared on the
right side of the equation
and then reduce the numbers with the gcf
32
it would be 32 over 80 squared times 100
is equals to sine 2 theta cancelling the
term on the right side
for the left side of the equation
multiply 32 over 80 squared with 100 or

02:10

100 over 1 in fraction
the product will be 3 200 over 80
squared evaluate the power it will be 3
200 over
four hundred
reduce the fraction with three thousand
two hundred the product shall be one
half is equals to sine two theta
the final step is to swap the sides of
the equation sine 2 theta is equals to
one-half
but we are not yet done what we have
accomplished is simply the value of sine

02:44

2 theta but not the angle which is
represented by theta to solve for the
remaining problem we shall use the
inverse function of sine
two theta is equals to inverse sine
of one half
calculate two theta is equals to pi
over six
divided by two the answer will be theta
is equals to pi over 12 or 15 degrees
so the answer will be the object shall

03:14

be directed at an angle of 15 degrees

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