a ball rolls 3.2m up a constant slope before it comes to a stop if the initial velocity of the ball was 2.2m/s how long does it take the ball to roll up the slope
To find the time it takes for the ball to roll up the slope, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
v is the final velocity (0 m/s because the ball comes to a stop)
u is the initial velocity (2.2 m/s)
a is the acceleration (due to gravity, which is -9.81 m/s^2 because the ball is rolling up the slope)
s is the distance the ball moves up the slope (3.2m)
Plugging in the values, we get:
0 = (2.2)^2 + 2(-9.81)(3.2)
0 = 4.84 - 62.784
-57.944 = -62.784
-57.944 / (-62.784) = t^2
t^2 ≈ 0.922
Taking the square root of both sides, we get:
t ≈ √0.922
t ≈ 0.960 s
Therefore, it takes the ball approximately 0.960 seconds to roll up the slope.