You have just landed on Planet X. You release a 100-g ball from rest from a height of 10.0 m and measure that it takes 3.40 s to reach the ground. Ignore any force on the ball from the atmosphere of the planet. How much does the 100-g ball weigh on the surface of Planet X?

w = 0.173 N

Explanation:

The weigh of any object is computed by multiplying its mass to the acceleration of gravity, so we need to find the gravity on that planet in order to compute the weigh we want.

The ball has a mass of 0.1 kg and its released from a height of 10 m, therefore it is in a free fall motion with gravity acting as a constant acceleration on the body, we can use the equations for free fall movement in order to determine the value for this acceleration:

y (t) = v_0 * t + y_0 - 0.5 * g * t^2

y (t) is the position in the end of the movement, when t = 3.4 s, so y (t) = 0 m.

v_0 is the initial velocity, in this case v_0 = 0 m/s.

y_0 is the initial position of the ball, in this case it is 10 m.

g is the gravity that we want to know.

Applying these values in the equation we have:

0 = 0 * (3.4) + 10 - 0.5*g * (3.4) ^2

0 = 10 - 0.5*11.56*g

0 = 10 - 5.78*g

5.78*g = 10

g = 1.73 m/s^2

Then we can use this value to find out the weigh of the ball in that planet:

w = g*m = 0.1*1.73 = 0.173 N