Problem 72 - University Physics with Modern Physics

Question

How fast would a \(5.00-\mathrm{g}\) fly have to be traveling to slow a \(1900 .-\mathrm{kg}\) car traveling at \(55.0 \mathrm{mph}\) by \(5.00 \mathrm{mph}\) if the fly hit the car in a totally inelastic head-on collision?

Step-by-Step Solution

Answer

Answer: The fly must be traveling at approximately 858720 m/s in the opposite direction to slow the car down by 5 mph.

Step 1: Understand the problem and write known values

First, let's write down the known values: Mass of fly (m1) = 5 g = 0.005 kg (convert grams to kilograms) Mass of car (m2) = 1900 kg Initial speed of car (v2) = 55 mph = 24.61 m/s (convert mph to m/s) Final speed of car (v2') = 50 mph = 22.35 m/s Initial speed of the fly is unknown, we will call it v1.

Step 2: Apply Conservation of Linear Momentum Principle

The conservation of linear momentum states that the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can write the equation: m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2' Note that after the collision, both the fly and the car move together hence they have the same final velocity. Therefore, v1' = v2'.

Step 3: Solve for the speed of the fly

Rearrange the equation from Step 2 to solve for v1: v1 = (m1 * v1' + m2 * (v2' - v2)) / m1 Substitute the known values and solve for v1: v1 = (0.005 * 22.35 + 1900 * (22.35 - 24.61)) / 0.005 v1 = (0.11175 - 4294) / 0.005 v1 ≈ -858720 m/s The negative sign indicates the fly is moving in the opposite direction to the car, which is expected in a head-on collision. The fly must be traveling at approximately 858720 m/s in the opposite direction to slow the car down by 5 mph.