ebo throws a ball into the air its velocity at the start is 18m/s at an angle of 37 degree to the ground
how can we workout the velocity as it lands and give our answers in component form
To determine the velocity of the ball as it lands, we need to break down its initial velocity into horizontal (x) and vertical (y) components.
Given:
Initial velocity (Vi) = 18 m/s
Angle to the ground (θ) = 37 degrees
To find the horizontal and vertical components, we can use basic trigonometry:
Horizontal component (Vx):
Vx = Vi * cos(θ)
Vertical component (Vy):
Vy = Vi * sin(θ)
Plugging the values into the formulas:
Vx = 18 m/s * cos(37°)
Vy = 18 m/s * sin(37°)
Now we have both components of velocity. To find the final velocity when the ball lands, we know that the vertical velocity at this point is the negative of the initial vertical velocity due to gravity. Thus, the vertical component of the velocity (Vy) becomes negative.
Therefore, the velocity when the ball lands can be written in component form as:
Vx = 18 m/s * cos(37°)
Vy = - (18 m/s * sin(37°))
To get the magnitude and direction of the resulting velocity, we can use the Pythagorean theorem and inverse trigonometric functions:
Magnitude of the velocity:
V = √(Vx^2 + Vy^2)
Direction of the velocity:
θ = tan^(-1)(Vy / Vx)
By substituting the values of Vx and Vy, you can calculate the magnitude and direction of the velocity as the ball lands.