Spaceship hit the ground with a velocity of 100 m/s

1. Jun 4, 2009

szekely

Ok so I'm in 7th grade and I think I'm pretty good in science class. The other day we had some math questions involving some equations. One question was something like a spaceship hit the ground with a velocity of 100 m/s and then it asked like what was its mass. This question also included the gravity of the planet (like 7.8 m/s squared). The next question was what was the force of the impact. The answer was something low because the force of gravity was 7.8. I was wondering how F=ma would work here because the velocity makes it seem like the impact would have much more force than what it was.

Then i started thinking about if you threw a ball straight up. As soon as it left your hand the acceleration would be downward at 9.8 because of gravity. So the acceleration upward is -9.8 even though its still going up. I know that if it hits something while going up its going to have a force so i don't see how F=ma works if acceleration is negative.

Just today i started wondering if this was because of momentum and if you would somehow get p=mv into there.

Thanks for all of the responses. I know this should be extremely easy for you guys.

2. Jun 4, 2009

SmashtheVan

Re: F=ma?

in these kinds of problems the negative sign is only there to denote direction, with up being the positive direction, and down being the negative(which im assuming is the convention being used for your class). This applies for forces, momentum, accelerations, velocities, etc.

3. Jun 5, 2009

atyy

Re: F=ma?

When the ball leaves your hand, a=-9.8m/ss. So it is slowing down. If it hits something on the way up, it will slow down even more quickly, so its deceleration increases to a>-9.8m/ss. This is due to whatever it hit exerting a force on the ball. By Newton's third law, the ball will exert the a force of the same magnitude on whatever it hit. To find out the force, one has to know the change in velocity during the impact, and the duration of the impact.

4. Jun 5, 2009

Integral

Staff Emeritus
Re: F=ma?

There must have been more to this question, you do not have enough information to find the mass.
If you knew the mass then the force of the impact would indeed be just $$F = ma$$ with the acceleration being that given.
When you throw the ball up it has velocity of +V and acceleration of -g that means (on earth) 9.81 ms-2 down. Since it is accelerating downward its upward velocity is always getting smaller, it is slowing down. When the velocity reaches zero the ball has reached its highest point. It still has a acceleration of -g, so now its velocity begins to increase downward. As it falls in the negative direction (down) its velocity increases due to the acceleration in the negitive direction. When it reaches the point of release its downward speed will equal the speed at which it was released initially. I carefully used the word speed here, since the velocities are not equal, Vup = - Vdown

Does this help?