19) a child on a sled starts from rest at the top of a 15.0° slope. if the trip to the bottom takes 15.2 s,
how long is the slope? assume that frictional forces may be neglected.

288.8 m

Explanation:

We have the following data:

is the time it takes to the child to reach the bottom of the slope

is the initial velocity (the child started from rest)

is the angle of the slope

is the length of the slope

Now, the Force exerted on the sled along the ramp is:

(1)

Where is the mass of the sled and its acceleration

In addition, if we draw a free body diagram of this sled, the force along the ramp will be:

(2)

Where is the acceleration due gravity

Then:

(3)

Finding :

(4)

(5)

(6)

Now, we will use the following kinematic equations to find :

(7)

(8)

Where is the final velocity

Finding from (7):

(9)

(10)

Substituting (10) in (8):

(11)

Finding :

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s