At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. at this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. when she lands, where will she find the ball? ignore air resistance.

Use this kinematics equation to the describe the vertical motion of the ball as a function of time:

H(t) = X + Vt + 0.5At²

H(t) is the height of the ball

X is the initial height of the ball

V is the initial vertical velocity of the ball

A is the vertical acceleration of the ball

Given values:

X = 100m

V = -2m/s

A = -9.81m/s² (constant acceleration due to gravity near the surface of the earth)

Plug in the values:

H(t) = 100 - 2t - 4.905t²

To find a time t for when the ball hits the ground, plug in H(t) = 0 and solve for t:

100 - 2t - 4.905t²

t = 4.316s, -4.724s

Reject the negative value because this doesn't make sense in the context of the question.

t = 4.316s

For the ball's horizontal motion under constant velocity:

X = VΔt

X is the horizontal distance traveled by the ball

V is the ball's velocity

Δt is the elapsed time

Given values:

V = 2.0m/s

Δt = 4.316s (from previous work)

Plug in and solve for X:

X = 2.0×4.316

X = 8.632m

The girl will find the ball 8.632m from where her hot air balloon will land.

if the forces acting on an object are unbalanced, the object will accelerate in the direction of the net force on the object.

explanation:

this is best explained by having an understanding of newton's second law, which states that f=ma. you see, when the forces are unbalanced, net force (sum of all forces) is not zero. therefore making it necessary for the object to have an acceleration in the direction of the net force.