A ball, initially at y = 0, is thrown straight down and takes 1.40 s to move 13.8 m in the - y direction. Calculate the initial velocity of the ball.
To calculate the initial velocity of the ball, we can use the kinematic equation:
y = y0 + v0t + (1/2)at^2
Where:
y = final position of the ball = -13.8 m (since it is moving in the -y direction)
y0 = initial position of the ball = 0 m
v0 = initial velocity of the ball
t = time taken by the ball = 1.40 s
a = acceleration of the ball = -9.8 m/s^2 (acceleration due to gravity)
Plugging in these values into the equation, we get:
-13.8 = 0 + v0(1.40) + (1/2)(-9.8)(1.40)^2
Simplifying the equation further:
-13.8 = 1.4v0 - 1/2(9.8)(1.96)
-13.8 = 1.4v0 - 9.615
Rearranging the terms:
1.4v0 = -13.8 + 9.615
1.4v0 = -4.185
Finally, solving for v0 (initial velocity):
v0 = -4.185 / 1.4
v0 ≈ -2.989 m/s
Therefore, the initial velocity of the ball is approximately -2.989 m/s.