In a shipping company distribution center, an open cart of mass 50 kg is rolling to the left at a speed of 5 m/s. You can ignore friction between the cart and the floor. A 15 kg package slides down a chute that makes an angle of 27 degrees below the horizontal. The package leaves the chute with a speed of 3 m/s, and lands in the cart after falling for 0.75 seconds. The package comes to a stop in the cart after 4 seconds. What is:

(1). 9.35 m/s.

(2).V2 = 3.22 m/s to the left.

Explanation:

So, we are given the following data or parameters or infomation in the question above as;

(1). "open cart of mass 50 kg is rolling to the left at a speed of 5 m/s. "

(2). "A 15 kg package slides down a chute that makes an angle of 27 degrees below the horizontal."

(3). "The package leaves the chute with a speed of 3 m/s, and lands in the cart after falling for 0.75 seconds."

(4). "The package comes to a stop in the cart after 4 seconds."

(a). So, in order to solve this question, we will be making use of the equations below;

(1). Gravitational potential energy = mass × acceleration due to gravity × height.

(2). Kinetic energy = 1/2 × mass × (velocity)^2.

(3). Kinetic energy (initial) + potential energy (initial) = kinetic energy (final) + potential energy (final).

So, starting from equation (1) above;

Gravitational potential energy = mass × acceleration due to gravity × height.

Gravitational potential energy = 15 × 9.8 × 4 = 588 J.

Kinetic energy = 1/2 × mass × (velocity)^2. = 1/2 × 15 × (3)^2.= 67.5 J.

kinetic energy (final) = 1/2 × 15 × v^2. = 7.5v^2.

Hence, Kinetic energy (initial) + potential energy (initial) = kinetic energy (final) + potential energy (final).

[potential energy (final) = 0].

67.5 + 588 = 7.5v^2.

v = 9.35 m/s

(b). -3 cos (27°) = -2.67 m/s.

15 × -2.67 + 50 × 5 =( 15 + 50) × v2.

=> 209.5 = 65v2.

=> V2 = 3.22 m/s to the left.

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.