Answer:
a) The speed of the ball at the bottom of the first plane is 2.59 m/s
b) It takes the ball 6.56 s to roll down the first plane.
Explanation:
The equations for the position and velocity of the ball are as follows:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position at time t
x0 = initial position
v0 = initial speed
t = time
a = acceleration
v = velocity at time t
b) First, let´s calculate the time it takes the ball to reach the bottom of the plane using the equation for the position:
x = x0 + v0 · t + 1/2 · a · t²
Placing the center of the frame of reference at the point where the ball starts rolling, x = 0. Since the ball starts from rest, v0 = 0. Then:
x = 1/2 · a ·t²
Let´s find the time when the ball reaches a position of 8.50 m
8.50 m = 1/2 · 0.395 m/s² · t²
t² = 2 · 8.50 m / 0.395 m/s²
t = 6.56 s
a) Now, using the equation of the velocity, we can calculate the velocity of the ball at the bottom of the plane (t = 6.56 s):
v = a · t
v = 0.395 m/s² · 6.56 s = 2.59 m/s
