Question

A sniper is sitting on top of a tower at a height of 60 ft. There are four work- ers
K
,
L
,
M
and
N
standing at a distance of
96
f
t
,
90
f
t
,
82
f
t
, and
75
f
t
respectively from the base of the tower. The heights of
K
,
L
,
M
, and
N
are
6
f
t
,
5.5
f
t
,
5.7
f
t
, and
5.2
f
t
respectively. The sniper misfires a bullet at an angle
θ
with the horizontal. Since the range covered by the bullet is short, the path of the bul- let is assumed to be a straight-line path. If
t
a
n
θ
=
2
3
, choose the correct option.


All workers are safe

All the workers are safe except
K

Only
K
and
N
are safe
No one is safe

Only
K
is safe

All the workers are safe except
M

Answer 1

all workers are safe

Step-by-step explanation:

S(0,60)

N(75,0)

M(82,0)

L(90,0)

K(96,0)

given, tan θ =  2/3 i.e. slope(m) = 2/3 = 0.67

find the slope of SN, SM, SL, SK

m(SK) = 0.625

Therefore SN,SM,SL,SK is inside the slope 2/3

                   THEREFORE all workers are safe

Answer 2

Answer:

Only K and N are Safe

Step-by-step explanation:

If tan = 2/3 then the angle made with horizontal is 33.69

This implies the angle made with verticle is 56.309

So, if the bullet fires from 60ft, Applying it should reach a distance of 90ft. (Tan =3/2 for verticle) (3/2= ft/60 therefore ft = 90ft) This eliminates K and K is safe.

Since the shot is fired 90ft L is directly a target at foot. So L is not safe

For M - (2/3 = x/82 this implies x = 54.66) But in reality height is 60ft. Difference is 5.4 but L is 5.5ft so L is directly shot in head.

And for N, he is safe If you imply the same above logic