Note: I am in Alegebra-based Physics.

You have landed on an unknown planet, Newtonia, and want to know what objects will weigh there. You find that when a certain tool is pushed on a frictionless horizontal surface by a 12.2 N force, it moves 16.3 m in the first 2.30 s, starting from rest. You next observe that if you release this tool from rest at 10.6 m above the ground, it takes 2.68 s to reach the ground.

What does the tool weigh on Newtonia?
Answer should be expressed in N.

What would it weigh on Earth?
Answer shoule be expressed in N.



On the horizontal, you know F=ma, and a= 2*distance/1sec^2.

solve for m.

In the vertical,

distancefell= 1/2 gravaccel*2.68^2
solve for accelerationdueto Gravity.

To find the weight of the tool on Newtonia, we need to determine its mass first. We can use the formula F = ma to find the mass of the tool on the horizontal. The force applied is 12.2 N, and the acceleration can be calculated using the formula a = 2 * distance / 1 sec^2, where the distance is 16.3 m.

Using the formula, we have:
12.2 N = m * (2 * 16.3 m) / (1 sec^2)

Simplifying, we get:
12.2 N = 32.6 m / sec^2 * m

To solve for the mass, we can rearrange the equation:
m = 12.2 N * sec^2 / (32.6 m)

Now, we can calculate the mass of the tool on the horizontal.

Next, let's find the acceleration due to gravity on Newtonia. We know that the distance fallen is 10.6 m, and it took 2.68 s to reach the ground. We can use the formula:

distance_fell = 1/2 * grav_acceleration * time^2

Plugging in the values, we have:
10.6 m = 1/2 * grav_acceleration * (2.68 s)^2

Simplifying, we get:
10.6 m = 3.4 * grav_acceleration * 7.1824 s^2

To isolate the acceleration due to gravity, we rearrange the equation:
grav_acceleration = 10.6 m / (3.4 * 7.1824 s^2)

Now, we have the acceleration due to gravity on Newtonia.

Finally, we can find the weight of the tool on Newtonia and Earth.

Weight on Newtonia = mass on Newtonia * grav_acceleration on Newtonia
Weight on Earth = mass on Earth * grav_acceleration on Earth

To convert the mass on Newtonia to weight, we need to multiply it by the gravitational acceleration on Newtonia, and the same for Earth.

Weight on Newtonia = mass on Newtonia * grav_acceleration on Newtonia
Weight on Earth = mass on Earth * grav_acceleration on Earth

Note that the gravitational acceleration on Newtonia may be different from the gravitational acceleration on Earth.