Kinematics in two dimension problem:
a baseball pitcher attempts to hit a falling bag of money by throwing a ball at it. the pitcher throws the ball with an initial velocity of v° (v knot) at an angle of ∅ above the horizontal at the same instant that the bag is dropped some distance away(see diagram). three seconds later, the ball hints the bag! what was the value of v° (v knot) and ∅ ?

∅ = 36.9°, v = 25m/s

Explanation:

Since the ball and the bag are affected by gravity in the same way, the pitcher has to aim the ball directly at the bag and the angle can be calculated by the tan∅ = 45m/60m.

The x-component of the velocity v is constant and can be calculated by:

vₓ= 60m/ 3s = 20m/s

The velocity v can be found from this equation:

v = vₓ/cos∅ = 25m/s

25 m/s, 36.9°

Explanation:

The vertical position of the bag at time t is:

y = y₀ + v₀ t + ½ at²

y = 45 + (0) t + ½ (-9.8) t²

y = 45 − 4.9 t²

The vertical position of the ball at time t is:

y = y₀ + v₀ t + ½ at²

y = 0 + (v₀ sin θ) t + ½ (-9.8) t²

y = (v₀ sin θ) t − 4.9 t²

The two are equal when t = 3.

45 − 4.9 (3)² = (v₀ sin θ) (3) − 4.9 (3)²

15 = v₀ sin θ

The horizontal position of the ball at 3 seconds is 60 m:

x = x₀ + v₀ t + ½ at²

60 = 0 + (v₀ cos θ) (3) + ½ (0) (3)²

20 = v₀ cos θ

Two equations, two unknowns.  First, divide the first equation by the second to find θ.

15/20 = (v₀ sin θ) / (v₀ cos θ)

0.75 = tan θ

θ ≈ 36.9°

Next, use Pythagorean theorem to find v₀.

v₀² = (v₀ cos θ)² + (v₀ sin θ)²

v₀² = 20² + 15²

v₀ = 25 m/s

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.