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.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles