A dive bomber has a velocity of 290 m/s at an angle θ below the horizontal. When the altitude of the aircraft is 2.15 km, it releases a bomb, which subsequently hits a target on the ground. The magnitude of the displacement from the point of release of the bomb to the target is 3.09 km. Find the angle θ.
Y = Vy(T) + (1/2)gT^2
X = Vx(T)
where
Y = distance of ground from point of release =2.15 km =2150 m
Vy = vertical component of the initial velocity = 290*sin Θ
Θ = angle of release with respect to the horizontal
T = time for bomb to reach the target
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
X = horizontal displacement of bomb from release point = 3.09 km = 3090 m
Vx = horizontal component of initial velocity = 290(cos Θ)
Substituting appropriate values,
2150 = 290(sin Θ)(T) + (1/2)(9.8)T^2
and simplifying,
2150 = 290(sin Θ)(T) + 4.9(T^2) -- call this Equation 1
For the horizontal component,
3090 = 290(cos Θ)T
Solving for "T"
T = 3090/(cos Θ)(290)
T = 10.6551/cos Θ
and substituting this in Equation 1,
2150 = 290(sin Θ)(10.65/cos Θ) + 4.9(10.65/cos Θ)^2
I can't seem to simplify this? Can you help me?