A student flings a 2.3g ball of putty at a 225g cart sitting on a slanted air track that is 1.5m long. The track is slanted at an angle of 25 degrees with the horizontal. If the putty is travelling at 4.2 m/s when it hits the cart, will the cart reach the end of the track before it stops and slides back down? Support your answer with calculations.

To determine whether the cart will reach the end of the track before it stops and slides back down, we need to compare the initial kinetic energy of the putty to the potential energy gained by the cart as it moves uphill on the track.

First, let's calculate the potential energy gained by the cart. The gravitational potential energy (PE) is given by the equation:

PE = mgh

Where m is the mass of the cart, g is the acceleration due to gravity, and h is the maximum height the cart reaches on the track. We can calculate h using the given angle of the track with the horizontal and the length of the track. By using trigonometry, we can find the vertical height (h) using the equation:

h = sin(angle) * length

Substituting the values, we get:

h = sin(25 degrees) * 1.5m

Now, let's calculate the potential energy gained by the cart:

PE = (225g) * (9.8m/s^2) * (sin(25 degrees) * 1.5m)

Next, let's calculate the initial kinetic energy of the putty. The kinetic energy (KE) is given by the equation:

KE = (1/2)mv^2

Where m is the mass of the putty and v is its velocity. We can calculate the initial kinetic energy as follows:

KE = (1/2)(0.0023kg)(4.2m/s)^2

Now, compare the potential energy gained by the cart and the initial kinetic energy of the putty. If the potential energy gained by the cart is greater than or equal to the initial kinetic energy of the putty, then the cart will reach the end of the track before it stops and slides back down.

Compare the calculated potential energy (PE) to the calculated initial kinetic energy (KE). If PE ≥ KE, the cart will reach the end of the track before stopping.

If PE < KE, the cart will not reach the end of the track before stopping.

Solve the above inequality to determine the outcome.