Question

at what speed do a bicycle and its rider, with a combined mass of 90 kg , have the same momentum as a 1600 kg car traveling at 4.8 m/s ? express your answer to two significant figures and include the appropriate units.

Answer 1

The bicycle and its rider would need to travel at approximately 85 m/s to have the same momentum as a 1600 kg car traveling at 4.8 m/s.

Step-by-step explanation:

To find the speed at which a bicycle and its rider, with a combined mass of 90 kg, have the same momentum as a 1600 kg car traveling at 4.8 m/s, we use the momentum equation:

Momentum = mass × velocity

First, we calculate the momentum of the car:

Momentum of car = 1600 kg × 4.8 m/s = 7680 kg·m/s

Since momentum is conserved, the momentum of the bicycle and rider must also equal 7680 kg·m/s. To find their velocity:

Velocity of bicycle and rider = Momentum / mass of bicycle and rider

Velocity of bicycle and rider = 7680 kg·m/s / 90 kg ≈ 85.33 m/s

To express this at two significant figures, the speed would be 85 m/s.

Answer 2

The momentum of an object is defined as the product of its mass and velocity. Therefore, we can set up an equation where the momentum of the bicycle and rider is equal to the momentum of the car:

(m_bicycle + m_rider)v_bicycle = m_carv_car

where m_bicycle and m_rider are the masses of the bicycle and rider (assumed to be combined), v_bicycle is the velocity of the bicycle and rider, m_car is the mass of the car, and v_car is the velocity of the car.

Substituting the given values, we get:

(90 kg)v_bicycle = (1600 kg)(4.8 m/s)

Solving for v_bicycle, we get:

v_bicycle = (1600 kg)(4.8 m/s)/(90 kg) = 85.3 m/s

Therefore, the bicycle and rider would have to travel at a speed of 85.3 m/s to have the same momentum as the car traveling at 4.8 m/s.