A 1-kg ball in the air has an initial velocity vo = [ 20 ] i + [ -30 ] j m/s. It falls for a total time of 1 s. Assume that positive x-values are to the right and positive y-values are upward.

A)What is the impulse or change in momentum Delta p of the ball?

B)What is the final momentum pf of the ball?

C)What is the initial kinetic energy Ki of the ball?

D)What is the final kinetic energy Kf of the ball?

E)What is the change in kinetic energy DeltaK of the ball?

F)What is the ball's change in height delta y after it falls 1 s?

To find the answers to these questions, we will need to use the concepts of impulse, momentum, and kinetic energy. Let's go step by step.

A) The impulse or change in momentum Δp of the ball can be calculated using the formula:

Δp = m * Δv

where m is the mass of the ball and Δv is the change in velocity. Since the ball is falling in the negative y-direction, the change in velocity is equal to its final velocity, as its initial velocity in the y-direction is already negative. Therefore, Δv = v_f - v_i = -30 - 0 = -30 m/s.

Substituting the values, we get Δp = 1 kg * (-30 m/s) = -30 kg*m/s (taking downward as the positive direction).

B) The final momentum pf of the ball can be calculated using the formula:

pf = m * v_f

where m is the mass of the ball and v_f is the final velocity. Since the ball is falling in the negative y-direction, its final velocity in the y-direction is -30 m/s.

Substituting the values, we get pf = 1 kg * (-30 m/s) = -30 kg*m/s (taking downward as the positive direction).

C) The initial kinetic energy Ki of the ball can be calculated using the formula:

Ki = 0.5 * m * v_i^2

where m is the mass of the ball and v_i is the initial velocity. Since the initial velocity is given as [20]i + [-30]j m/s, we need to consider only the magnitude of the initial y-component of velocity for kinetic energy.

Substituting the values, we get Ki = 0.5 * 1 kg * (-30 m/s)^2 = 450 J.

D) The final kinetic energy Kf of the ball can be calculated using the formula:

Kf = 0.5 * m * v_f^2

where m is the mass of the ball and v_f is the final velocity. Since the final velocity in the y-direction is given as -30 m/s, we need to consider only the magnitude of the final y-component of velocity for kinetic energy.

Substituting the values, we get Kf = 0.5 * 1 kg * (-30 m/s)^2 = 450 J.

E) The change in kinetic energy ΔK of the ball can be calculated as:

ΔK = Kf - Ki

Substituting the values, we get ΔK = 450 J - 450 J = 0 J.

F) The change in height Δy after the ball falls for 1 s can be calculated using the following formula:

Δy = v_i * t + 0.5 * g * t^2

where v_i is the initial velocity in the y-direction, t is the total time of 1 s, and g is the acceleration due to gravity (-9.8 m/s^2).

Substituting the values, we get Δy = (-30 m/s) * 1 s + 0.5 * (-9.8 m/s^2) * (1 s)^2 = -34.9 m (taking downward as the positive direction).

Therefore, the change in height Δy after the ball falls for 1 s is approximately -34.9 meters.