A) The longest horizontal distance is reached at 45 degrees angle. This is true for any projectile launch.
B) First, calculate fligth time (using the vertical motion) and then calculate the horizontal movement.
Flight time = 2* ascendent time
ascendent time => final vertical velocity, Vy, = 0
sin(45) = Voy / Vo => Voy = Vosin(45) = 25.5 m/s * (√2) / 2 = 18.03 m/s
Vy = Voy - gt = 0 => Voy = gt = t = Voy / g
Use g = 10 m/s^ (it is an aproximation, because the actual value is about 9.81 m/s^2 depending on the latitud)
t = 18.03 m/s / 10 m/s^2 = 1.83 s
This is the ascendant time going upward.
The flight time is 2*1.83 = 3.66 s
Horizontal motion
Horizontal velocity = Vx = constant = Vox = Vo*cos(45) = 18.03 m/s
Vx = x / t => x = Vx*t
Horizontal distance = xmax = 18.03m/s*3.66 s = 65.99 m
c) The time the ballon will be in the air was calculated in the part B, it is 18.03 s
They are able to have the same value as the negative sign is simply transferred to the inside. Either way 4 is being subtracted from 3.
Since we will be completing the square we need to isolate the x
y-5 = 2x^2 -4x
now we the coefficient of the x^2 to equal 1 so we take 2 as common factor
y-5 = 2(x^2 -2x)
now we'll make it perfect square by adding 2 to both sides
y-5+2=2(x^2-2x+1)
now simplify and convert the right side to squared expression
y-3 = 2(x-1)^2
now isolate the y
y = 2(x-1)^2 +3 that's it
Answer:
30.9°
Step-by-step explanation:
Right Angle Triangle = 90°
59.1 + ? = 90
90 - 59.1 = 30.9
