Question

Find the ratio of pA/pB, when A is a 5.0 kg rock falling 10 meters to the ground and B is a 1.0 kg apple falling 10 meters to the ground.(Compare their momenta just before they hit the ground.)

Answer 1

pA/pB = 5.00

Step-by-step explanation:

To find the ratio pA/pB you first calculate the velocities of both rocks just before they hit the ground. You use the following formula:

`v^2=v_o^2+2gy` (1)

vo: initial velocity = 0

g: gravitational acceleration = 9.8m/s^2

y: height = 10m

The parameters y, g and vo are the same for both rocks, hence the velocity is the same, v = vA = vB. Next, it is not necessary to calculate the velocities because these are canceled in the ration for the momentum:

`(p_A)/(p_B)=(m_Av_A)/(m_Bv_B)=(m_A)/(m_B)`

finally, you replace the values of the masses and you obtain:

`(p_A)/(p_B)=(m_A)/(m_B)=(5.0kg)/(1.0kg)=5.0`

hence, the ratio is 5.0