an aeroplane takes of at an angle of 45deg to the horizontal. If the vertical component of its velocity is 300kmph, Calculate its actual velocity. what is the horizontal component of it velocity?

what is 300/sin45? what is 300tan45?

300km/h

To calculate the actual velocity of the airplane, we can use the given information about the vertical component of its velocity and the angle at which it takes off. We can use trigonometric functions to solve this problem.

First, let's calculate the actual velocity of the airplane using the vertical component of its velocity. Given that the vertical component of velocity is 300 km/h, we need to convert it to meters per second (m/s) for consistency in units.

1 km/h = 1000/3600 m/s (conversion factor)
Therefore, the vertical component of velocity is:
300 km/h = (300 * 1000/3600) m/s = 83.33 m/s (rounded to two decimal places)

Since the angle of takeoff is 45 degrees, we can use the trigonometric function sine (sin) to find the ratio between the vertical and actual velocities. The sine function is defined as the ratio of the opposite side to the hypotenuse in a right-angle triangle.

sin(angle) = opposite/hypotenuse

Let's represent the vertical component as "Vv" and the actual velocity as "V."
sin(45 degrees) = Vv/V

Rearranging the equation to solve for V:
V = Vv / sin(45 degrees)

Plugging in the values:
V = 83.33 m/s / sin(45 degrees)

Using a scientific calculator, we can find the sine of 45 degrees:
sin(45 degrees) = 0.7071 (rounded to four decimal places)

Now, we can calculate the actual velocity:
V = 83.33 m/s / 0.7071 ≈ 117.88 m/s (rounded to two decimal places)

Therefore, the actual velocity of the airplane is approximately 117.88 m/s.

To calculate the horizontal component of its velocity, we can use the trigonometric function cosine (cos), which represents the ratio between the horizontal and actual velocities.

cos(angle) = adjacent/hypotenuse

Let's represent the horizontal component as "Vh."
cos(45 degrees) = Vh / V

Rearranging the equation to solve for Vh:
Vh = cos(45 degrees) * V

Plugging in the known values:
Vh = cos(45 degrees) * 117.88 m/s

Using a scientific calculator, we can find the cosine of 45 degrees:
cos(45 degrees) = 0.7071 (rounded to four decimal places)

Now, we can calculate the horizontal component of velocity:
Vh = 0.7071 * 117.88 m/s ≈ 83.33 m/s (rounded to two decimal places)

Therefore, the horizontal component of its velocity is approximately 83.33 m/s.