Two spacecraft are 13,500 m apart and moving directly toward each other. spacecraft#1 has velocity 525 m/s and accelerates at a constant -15.5 m/s2. they want to dock, which means they have to arrive at the same position at the same time with zero velocity. these aliens are watching in anticipation. (a) what should the initial velocity of the spacecraft#2 be? (b) what should be #2 constant acceleration?

-272 m/s, 8.03 m/s²

Explanation:

Let's call position 0 the point where the two spacecrafts meet.  Let's say spacecraft #1 starts x units to the left of 0 and spacecraft #2 starts 13500-x units right of 0.

For spacecraft #1:

v = 0 m/s

v₀ = 525 m/s

a = -15.5 m/s²

x = 0 m

x₀ = -x

The distance that spacecraft #1 travels is:

v² = v₀² + 2a(x - x₀)

(0 m/s)² = (525 m/s)² + 2(-15.5 m/s²)(0 m − -x)

0 = 275625 − 31x

x ≈ 8891 m

The time it takes to reach 0 velocity is:

v = at + v₀

0 m/s = (-15.5 m/s²) t + 525 m/s

t ≈ 33.87 s

For spacecraft #2:

v = 0 m/s

x = 0 m

x₀ = 13500-x ≈ 4609 m

t = 33.87 s

Using the same equations:

v² = v₀² + 2a(x - x₀)

(0 m/s)² = v₀² + 2a(0 m − 4609 m)

0 = v₀² − 9218a

v = at + v₀

0 m/s = a(33.87 s) + v₀

0 = 33.87a + v₀

Now we have two equations and two variables.  We can solve the system of equations.

First, let's solve for a and substitute:

0 = 33.87a + v₀

a = -v₀ / 33.87

0 = v₀² − 9218 (-v₀ / 33.87)

0 = v₀² + 272 v₀

0 = v₀ (v₀ + 272)

v₀ = -272 m/s

Now we can find the acceleration:

a = -(-272) / 33.87

a = 8.03 m/s²

choosing tennis and golf balls is your inde choice.

their mass and volume are dep

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.