An airplane takes off at a constant speed of 331 m/s at an angle of 45 degrees. What is the airplane's horizontal velocity

To find the airplane's horizontal velocity, we can break down the initial velocity vector in terms of its horizontal and vertical components.

The horizontal component of the velocity can be calculated using the formula:
horizontal velocity = initial velocity * cos(angle)

In this case, the initial velocity is given as 331 m/s and the angle is 45 degrees. Let's calculate it:

horizontal velocity = 331 m/s * cos(45 degrees)

To evaluate cos(45 degrees), we can use the trigonometric values from a unit circle or a calculator. The value of cos(45 degrees) is 0.7071 (rounded to four decimal places):

horizontal velocity = 331 m/s * 0.7071

Now we can multiply the two values together:

horizontal velocity ≈ 233.0569 m/s

Therefore, the airplane's horizontal velocity is approximately 233.0569 m/s.

To find the airplane's horizontal velocity, we need to determine the horizontal component of the velocity.

The horizontal component of velocity can be found using trigonometry. In this case, the given angle of 45 degrees is with respect to the horizontal direction.

The horizontal velocity (Vx) can be calculated using the formula:

Vx = V * cos(angle)

where:
V = total velocity (331 m/s)
angle = angle with respect to the horizontal direction (45 degrees)

Plugging in the given values, we can calculate the horizontal velocity:

Vx = 331 m/s * cos(45 degrees)

To evaluate this expression, we need to convert the angle from degrees to radians, as most mathematical functions in programming languages require the input in radians.

Angle in radians = angle in degrees * pi / 180

Using this conversion, we can rewrite the formula as:

Vx = V * cos(angle in radians)

Vx = 331 m/s * cos(45 degrees * pi / 180)

Vx = 331 m/s * cos(45 * π / 180)

Vx = 331 m/s * cos(0.7854)

Evaluating the expression further, we find:

Vx ≈ 331 m/s * 0.7071

Vx ≈ 234.0817 m/s

Therefore, the airplane's horizontal velocity is approximately 234.0817 m/s.