Object falling due to Gravity Problem

In summary, the lander is descending to land on the moon and the engine is cut off when it is 5.0 m above the surface with a downward speed of 0.8 m/s. The object is then in free fall and the speed of the lander just before it touches the surface can be found using the kinematic equation v^2 = v_o^2 + 2g(y-y_o), with a downward acceleration of 1.6 m/s^2. After correcting for the negative sign and using the correct units, the calculated speed is 4.08 m/s.
  • #1
mopar969
201
0
A lander is descending to land on the moon. 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. Please help me start with this problem thanks.
 
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  • #2
When an object is in free fall, only the gravity force is acting on it. So what is its downward acceleration? Use one of the kinematic equations to solve for its speed.
 
  • #3
I used the equation V = V0 + 2a(y-y0)
= (0.8)+2(1.6)(0-5)
= -15.2 m/s

Please check and make sure that I used the right equation and obtained the correct answer.
 
  • #4
Correct your equation...check units...it's v^2 = etc...
Also, be careful of plus and minus signs ...since you chose down as positive for initial velocity and acceleration, then the displacement down is also positive.
 
  • #5
Okay but now what do I do becase I would have a square root of a negative which is not possible?
 
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  • #6
Well, look it up...it's v_f^2 = v_o^2 + 2a(delta y), for constant acceleration...or you can derive it from the calculus...best to memorize it, once you know its derivation.
 
  • #7
mopar969 said:
Okay but now what do I do becase I would have a square root of a negative which is not possible?
Again, watch your plus and minus signs..
it's v^2 =v_o^2 + 2g(y - y_o); Since you chose down as positive, then (y - y_o) is (5- 0) = + 5. If you chose up as positive, then its v^2 = (-V_o)^2 + 2(-g)(-5 -0), which yields the same result. Those plus and minus signs will try to get you every time..don't let them.:wink:
 
  • #8
Thanks for the negative sign help. After I fixed everything I obtained an answer of 4.08 m/s. Can you tell me if my answer is correct. Thanks.
 
  • #9
mopar969 said:
Thanks for the negative sign help. After I fixed everything I obtained an answer of 4.08 m/s. Can you tell me if my answer is correct. Thanks.

it is correct.
 

1. What is the formula for calculating the velocity of an object falling due to gravity?

The formula for calculating the velocity of an object falling due to gravity is v = gt, where v is the velocity in meters per second, g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds.

2. How does the mass of the object affect its acceleration due to gravity?

The mass of an object does not affect its acceleration due to gravity. All objects, regardless of their mass, accelerate towards the Earth at a rate of 9.8 m/s^2 due to the force of gravity.

3. What is the difference between weight and mass in relation to an object falling due to gravity?

Weight is a measure of the force of gravity acting on an object, while mass is a measure of the amount of matter in an object. The weight of an object can change depending on the strength of the gravitational field, but the mass remains constant.

4. How does air resistance affect the speed of an object falling due to gravity?

Air resistance, also known as drag, can slow down the acceleration of an object falling due to gravity. This is because as the object falls, it collides with air molecules, creating a force in the opposite direction of its motion. The greater the surface area of the object, the more air resistance it experiences, resulting in a slower acceleration.

5. Is there a limit to how fast an object can fall due to gravity?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it. As an object falls, the force of gravity acting on it increases, resulting in an increase in acceleration. However, as the object reaches terminal velocity, the acceleration decreases and the object falls at a constant speed. Therefore, there is a limit to how fast an object can fall due to gravity (typically around 200 km/h for a human body).

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