Accelerating Car Homework: Find Velocity After 1m

[TheTank]

Homework Statement

A model car weighs 17N and is accelerated from rest by a 1cm diameter water jet moving at u=75m/s. Neglect all friction, find the velocity of the car after is has moved 1m.

Homework Equations

Reynold's
$$\sum{\vec{F}}=\int_{CS}{\rho\vec{V}(\vec{V_{rel}}\cdot \vec{n})dA}$$

The Attempt at a Solution

$$\sum{F}=\rho A (u-v)(u+v) + \rho A(u-v)(u-v)$$ => $$\sum{F}=-2A\rho uv$$
$$E_{k}=0.5mv^2 =\int^1_0 F \cdot ds=\frac{2\pi D^2 \rho uv \cdot s}{4}$$ => $$v=\frac{\rho u D^2 \pi s}{m}$$

I get the wrong answere when i put in the numbers.. v should be 25m/s

 

[mark726]

First, let's make sure we have all the necessary information. We have the weight of the car (17N), the diameter of the water jet (1cm), and the initial velocity of the water jet (75m/s). However, we are missing the mass of the car (m) and the distance it has traveled (s). Without these values, we cannot accurately solve for the final velocity of the car.

Assuming that the mass of the car is 1kg (based on the weight of 17N), we can use the formula for kinetic energy (E_k = 0.5mv^2) to solve for the velocity after the car has moved 1m.

E_k = 0.5mv^2
0.5(1kg)v^2 = 17J (since 1N = 1kg*m/s^2)
v^2 = 34m^2/s^2
v = √(34) ≈ 5.83m/s

Therefore, the final velocity of the car after moving 1m is approximately 5.83m/s. This is significantly lower than the expected value of 25m/s, so it is possible that there is a mistake in the given information or in the calculations. It would be helpful to double check the values and equations used to ensure accuracy.