To find the horizontal displacement and vertical displacement of a ball thrown from a cliff, we can use the equations of motion.
The horizontal displacement can be found using the formula:
Horizontal Displacement = Initial velocity * Time * Cos(angle)
The vertical displacement can be found using the formula:
Vertical Displacement = (Initial velocity * Time * Sin(angle)) + (0.5 * Acceleration * Time^2)
Given:
Initial velocity (Vi) = 15 m/s
Angle (θ) = 20° below the horizontal
Time (t) = 2.3 sec
First, let's convert the angle from degrees to radians, as trigonometric functions typically use radians.
θ = 20° * (π / 180°) ≈ 0.3491 radians
Now, we can calculate the horizontal displacement (a) and vertical displacement (b):
(a) Horizontal Displacement = Vi * t * Cos(θ)
Horizontal Displacement = 15 m/s * 2.3 sec * Cos(0.3491)
Horizontal Displacement ≈ 30.0694 m
(b) Vertical Displacement = (Vi * t * Sin(θ)) + (0.5 * g * t^2)
We need the acceleration due to gravity (g), which is approximately 9.8 m/s^2
Vertical Displacement = (15 m/s * 2.3 sec * Sin(0.3491)) + (0.5 * 9.8 m/s^2 * (2.3 sec)^2)
Vertical Displacement ≈ 6.65 m
Therefore, the horizontal displacement is approximately 30.0694 meters, and the vertical displacement 2.3 seconds later is approximately 6.65 meters.