physics question.....what is speed?

Question

A lunar lander is making its descent to Moon Base I. The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 m above the surface and has a downward speed of 0.8 m/s. With the engine off, the lander is in free fall.

What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is 1.6 m/s^2

i have no idea how to even approach the problem.....please help

Answer 1

The speed is zero.

Answer 2

Values you know:

v(initial) = -0.8 m/s (negative because it is going that fast downward)

d = -5.0 m (the ship will move downward that far)

a = -1.6 m/s^2 (negative because gravity points down to the ground, a negative direction)

The difference between speed and velocity is that speed is just a number; it does not care about direction.

Value wanted: Speed = | v(final) | (absolute value because we don't care about direction)

We do not know how much time is involved, nor do we care.

So, from the constant acceleration equations we know, the one not involving time is:

v(final)^2 - v(initial)^2 = 2 * a * d

so, v(final)^2 = 2 * -1.6 * -5.0 + (-0.8)^2

v(final) = 4.08 m/s in the downward direction

Answer 3

♦ at the moment you cut off your energy is E=E1 +E2, where E1=mgh is potential energy above the moon, E2=0.5m*v^2 is kinetic energy, m is your mass, h=5m, v=0.8m/s;
♦ hitting the moon’s ground you’ll have kinetic energy E=0.5m*u^2;
♣ my beer buddy Isaac once said energy conserves, he meant E=E,
that is mgh +0.5m*v^2 = 0.5m*u^2, hence 2gh+v^2 = u^2,
hence u=√(2gh+v^2) =√(2*1.6*5 +0.8^2) =4.08 m/s;
♥ if your teacher did not give you yet energies click me, I do it another way!