A girl throws a ball at a fence 10m away. The ball is 2m from the ground when it
leaves her hand with an initial velocity of v=8 i+8 j m/s. When the ball hits the
fence its horizontal velocity component is reversed (the vertical velocity component
is unchanged). Where does the ball hit the ground?
Calculat the distance d (metres) it hits the ground when there is no wall. Use reflection to calculate the bounce off the wall.
Then
case 1: if d>10 m.
Ball hits ground at (d-10) before the wall.
case 2: if d<10 m.
Ball hits ground at d m. from the girl.
To find the point where the ball hits the ground, we need to analyze the motion of the ball in both the horizontal and vertical directions.
First, let's consider the horizontal motion. Since the horizontal velocity component is reversed when the ball hits the fence, it will travel a distance of 10m from its initial position. The horizontal velocity component remains unchanged throughout the motion, which is given as 8i m/s.
Using the time, we can calculate the horizontal distance traveled by the ball using the equation: distance = velocity x time.
Since the velocity in the horizontal direction remains constant, the horizontal distance traveled can be calculated using the horizontal component of the velocity (v_x) and the time of flight (t).
Now, let's analyze the vertical motion of the ball. The initial vertical position of the ball is 2m above the ground, and its vertical velocity component (v_y) remains unchanged throughout the motion. We can use the equation of motion for vertical motion: h = v_y * t + (1/2) * g * t^2, where h is the vertical distance traveled, v_y is the vertical component of initial velocity, t is the time of flight, and g is the acceleration due to gravity.
At the point where the ball hits the ground, the vertical position (h) will be zero.
To find the time of flight (t), we can use the equation: t = h / v_y, where h = 2m and v_y = 8j m/s.
Using the calculated time of flight (t), we can substitute it into the equation for horizontal distance to find the point where the ball hits the ground.
First, let's find the time of flight (t):
t = h / v_y
t = 2m / 8j m/s
Next, let's calculate the horizontal distance traveled (d):
d = v_x * t
d = (8i m/s) * (2m / 8j m/s)
The horizontal distance traveled will give us the x-coordinate of the point where the ball hits the ground. Since the vertical position is zero at this point, the y-coordinate will be zero as well.
Thus, the ball hits the ground at the coordinates (d, 0).