Two objects are dropped from rest from the same height. Object A falls through a distance Da and during a time t, and object B falls through a distance Db during a time 2t. If air resistance is negligible, what is the relationship between Da and Db?
a. dA = ¼ dB.
b. dA = ½ dB.
c. dA = 2 dB.
d. dA = 4 dB.

a. Da = ¼ Db

Explanation:

Let us write out equations of motion for both objects:

For object A:

Since initial velocity, u =, is zero:

---------------------------------------- (1)

For object B:

Since initial velocity, u =, is zero:

---------------------------------------- (2)

Note: g = acceleration due to gravity

To get the relationship between Da and Db, we make g subject of formula in (1) and (2) and then equate:

From (1):

From (2):

Equating:

=>

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.

the maxium height is 34m/s