A bullet fired from A with a velocity of 900 ft/s must hit the target at B. Given the position of B with respect to A, find the angle q with which the bullet must be fired?
a. 30.50,
65.50
b. 28.50, 59.50
c. 32.50, 68.50
d. 34.50,
70.50
Let t be the time taken for the bullet to reach B
The horizontal distance
travelled by the bullet is given by
x = vx t
where x = 16000 ft and vx = 900 cos q
t = x/vx
The vertical distance
travelled is given by
y = vy(t) - (1/2)(g)t2
where y = 300 ft, vy = 900 sin q
and g = 32.2 ft/s2
=> 3000 = 16000 tan q - 5088 (1 + tan2
q)
tan2 q - 3.145 tan q
+ 1.6 = 0
The roots of the above equation are
tan q = 0.638 and tan q
= 2.538
q = 32.50 or 68.50
The bullet must be fired at an angle of 32.50 or 68.50