A stone is thrown from a cliff top with a vertical velocity of 50 m/s and horizontal velocity of 20 m/s.
What is its resultant velocity?
At what angle above the horizontal is it thrown?
Xo = hor. = 20m/s.
Yo = ver. = 50m/s.
tanA = Yo / Xo = 50 / 20 = 2.5,
a = 68.2 Deg.
Vo = Xo / cosA = 20 / cos68.2 = 53.85m/s @ 68.2 deg.
To find the resultant velocity, we can use the Pythagorean theorem. The resultant velocity is the vector sum of the vertical and horizontal velocities.
The vertical velocity is given as 50 m/s, and the horizontal velocity is given as 20 m/s.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √(vertical velocity^2 + horizontal velocity^2)
= √(50^2 + 20^2)
= √(2500 + 400)
= √2900
≈ 53.85 m/s
Therefore, the resultant velocity is approximately 53.85 m/s.
To find the angle above the horizontal at which the stone is thrown, we can use trigonometry. The angle can be found using the inverse tangent function (tan^-1) of the ratio of the vertical velocity to the horizontal velocity.
Angle = tan^-1(vertical velocity / horizontal velocity)
= tan^-1(50 / 20)
= tan^-1(2.5)
Using a calculator, we can find that the angle is approximately 68.2 degrees.
Therefore, the stone is thrown at an angle of approximately 68.2 degrees above the horizontal.
To find the resultant velocity, you need to use vector addition. The vertical and horizontal components of the velocity can be combined using the Pythagorean theorem and trigonometry.
Step 1: Find the magnitude of the resultant velocity.
The magnitude of the resultant velocity can be found using the Pythagorean theorem:
resultant velocity = sqrt(vertical velocity^2 + horizontal velocity^2)
resultant velocity = sqrt((50 m/s)^2 + (20 m/s)^2)
resultant velocity = sqrt(2500 m^2/s^2 + 400 m^2/s^2)
resultant velocity = sqrt(2900 m^2/s^2)
resultant velocity ≈ 53.85 m/s (rounded to two decimal places)
Step 2: Find the angle above the horizontal.
The angle above the horizontal can be found using trigonometry.
angle = atan(vertical velocity / horizontal velocity)
angle = atan(50 m/s / 20 m/s)
angle ≈ 68.2 degrees (rounded to one decimal place)
Therefore, the resultant velocity of the stone is approximately 53.85 m/s, and it is thrown at an angle of approximately 68.2 degrees above the horizontal.