Anthony and sissy are participating in the "roll-a-rama" rollerskating dance championship. while 75.6 kg anthony rollerskates backwards at 3.7 m/s, 59 kg sissy jumps into his arms with a velocity of 5.4 m/s in the same direction. how fast does the pair roll backwards together? answer to the nearest tenth of a m/s.

4.4 m/s

Explanation:

momentum is always conserved so we can use conversation of momentum to solve the question, also momentum is a vector quantity ( it has magnitude and direction) which is the product of the bodies mass and velocity.

conservation law of momentum relates by the formula below:

momentum before collision = momentum after collision

M1U1 + M2U2 = M1V1 + M2V2

in the case of this two, the formula becomes

M1U1 + M2U2 = V (M1 + M2) since she jumped into his arm

there masses are M1 = 75.6 kg M2 = 59 kg and their velocities are  U1 = 3.7 m/s and U2 = 5.4 m/s, their common velocity after collision = V since their motion is backward the formula becomes

-M1U1 - M2U2 = V(M1 + M2)

substitute the values into the equations

(-75.6 × 3.7 ) + (- 59 × 5.4) = V ( 75.6 + 59)

- 598.32 = 134.6 V

divide both side by 134.6

V = - 598.32 / 134.6 = -4.445 m/s  = -4.4 m/s to nearest tenth the negative means in the same backward direction

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.