Mary is standing at the top of a hill admiring the view. The hill is at a 4.70 degree tilt. 27.0m down the hill an old man let’s go of a stroller with a baby inside it. The stroller starts to roll downhill with its frictionless wheels. Mary starts to run after it with her best acceleration of 2.50 m/s/s. How far has the stroller rolled before she catches it
To find out how far the stroller has rolled before Mary catches it, we need to determine the time it takes for her to catch up with the stroller.
First, let's break down the forces acting on the stroller:
1. The force due to gravity, which pulls the stroller down the hill.
2. The normal force, which is perpendicular to the hill and cancels out the vertical component of gravity.
3. The force of friction, which is assumed to be zero since the wheels of the stroller are frictionless.
Since there is no friction to counteract the pull of gravity, the acceleration of the stroller is equal to the acceleration due to gravity, which is approximately 9.8 m/s².
Next, we can determine the time it takes for Mary to catch up with the stroller using the following equations of motion:
For the stroller:
1. Downward acceleration: a = 9.8 m/s² (acceleration due to gravity)
2. Distance traveled: d
For Mary:
1. Acceleration: a = 2.50 m/s²
2. Initial velocity: u = 0 m/s
3. Final velocity: v (which is equal to the velocity of the stroller when Mary catches up)
4. Time: t
We can use the second equation of motion, d = ut + (1/2)at², for both the stroller and Mary, equating them and solving for t:
d = ut + (1/2)at²
27.0m (the distance traveled by the stroller) = 0 + (1/2)(9.8 m/s²)t²
t² = (2 * 27.0 m) / 9.8 m/s²
t² = 54.0 m / 9.8 m/s²
t² ≈ 5.51 s²
t ≈ √(5.51)
t ≈ 2.35 s
Now we have the time it takes for Mary to catch up with the stroller. To find out the distance the stroller has rolled, we can use the equation of motion for the stroller:
d = ut + (1/2)at²
d = 0 + (1/2)(9.8 m/s²)(2.35 s)²
d ≈ 27.49 m
Therefore, the stroller has rolled approximately 27.49 meters before Mary catches it.