A soccer ball is released from the top of a smooth incline. After 3.90 s the ball travels 10.0 m. One second later it has reached the bottom of the incline. Assume the ball's acceleration is constant and determine its value ( m/s2).

Question

A soccer ball is released from the top of a smooth incline. After 3.90 s the ball travels 10.0 m. One second later it has reached the bottom of the incline. Assume the ball's acceleration is constant and determine its value ( m/s2).

How long is the incline?

Answer 1

d = 0.5a*t^2 = 10 m.

0.5a*3.9^2 = 10.
0.5a = 0.657.
a = 1.31 m/s^2.

L = 0.5*a*t^2.
a = 1.31 m/s^2.
t = 3.9 + 1 = 4.9 s.
L = ?

Answer 2

To determine the length of the incline, we can use the distance traveled by the soccer ball in a given time. We know that after 3.90 seconds, the ball has traveled a distance of 10.0 meters.

Using the formula for distance traveled with constant acceleration:

𝑑 = 𝑣0𝑡 + 1/2𝑎𝑡^2

Where:
𝑑 = distance traveled
𝑣0 = initial velocity (0 in this case, as the ball is released from rest)
𝑡 = time
𝑎 = acceleration

Plugging in the values we know:
10.0 m = 0 * 3.90 s + 1/2 * 𝑎 * (3.90 s)^2

Simplifying the equation:
10.0 m = 1/2 * 𝑎 * (3.90 s)^2

Now we can solve for the acceleration (𝑎):

𝑎 = 2 * 10.0 m / ((3.90 s)^2)

Calculating the value:
𝑎 ≈ 0.136 m/s^2

Therefore, the acceleration of the soccer ball is approximately 0.136 m/s^2.

Answer 3

To determine the length of the incline, we can first calculate the time it took for the ball to reach the bottom. We know that after 3.90 seconds, the ball traveled 10.0 meters.

Using the formula for distance traveled with constant acceleration:

d = v₀t + (1/2)at²

Where:
- d is the distance traveled (10.0 m)
- v₀ is the initial velocity (0 m/s, as the ball was released from rest)
- t is the time taken (3.90 s)
- a is the acceleration

We can rearrange the formula to solve for the acceleration:

a = (2d - 2v₀t) / t²

Plugging in the values we know:

a = (2 * 10.0 m - 2 * 0 m/s * 3.90 s) / (3.90 s)²
a = 20.0 m / 15.21 s²
a ≈ 1.31 m/s²

Therefore, the acceleration of the ball is approximately 1.31 m/s².

Now, to determine the length of the incline, we can use the uniformly accelerated motion equation:

v = v₀ + at

At the bottom of the incline, the ball has reached its final velocity and has traveled for 4.90 seconds. Plugging in the values:

v = 0 m/s + (1.31 m/s²)(4.90 s)
v ≈ 6.41 m/s

Now, we can use the formula for distance traveled with constant velocity:

d = v₀t

Where:
- d is the distance traveled (length of the incline)
- v₀ is the initial velocity (0 m/s)
- t is the time taken (4.90 s)

Plugging in the values:

d = 0 m/s * (4.90 s)
d = 0 m

The length of the incline is 0 meters. This indicates that the ball was released horizontally from the top of the incline and it traveled in a straight line.