To determine the vertical component of the velocity of an aircraft taking off at a certain angle, we need to use trigonometry. The vertical component can be calculated by multiplying the total velocity by the sine of the takeoff angle.
Given: Takeoff angle (θ) = 30 degrees Total velocity (V) = 500 km/hr
To find the vertical component (V_vertical), we can use the following formula:
V_vertical = V * sin(θ)
Let's substitute the values into the formula and calculate the result:
V_vertical = 500 km/hr * sin(30 degrees)
To perform the calculation, we need to convert the angle from degrees to radians because the trigonometric functions in most programming languages operate on radians.
1 degree = π/180 radians
30 degrees = (30 * π)/180 radians = π/6 radians
V_vertical = 500 km/hr * sin(π/6)
Using the approximate value of sin(π/6) = 0.5, we have:
V_vertical = 500 km/hr * 0.5 V_vertical = 250 km/hr
Therefore, the vertical component of the velocity of the aircraft will be 250 km/hr.