What Is the Minimum Speed Required for a Car to Jump Over Eight Cars?

[fattydq]

A student driver wants to make his car jump over eight cars parked side by side below a horizontal ramp. The vertical height of the ramp is 1.50 m above the cars, and the horizontal distance he must clear is 20 m. If the ramp is tilted upward so that the “takeoff angle” is 10° above the horizontal, what is the necessary minimum speed?

I honestly don't even know where to begin with this problem. Could someone help me out?

 

[kuruman]

This is a projectile motion problem. What have you learned about solving projectile motion problems?

 

[tomcue]

I can help you solve this problem by using the principles of physics. To determine the minimum speed for the car to successfully jump over the eight cars parked below the ramp, we need to consider the conservation of energy and the laws of motion.

First, we can calculate the initial potential energy of the car at the top of the ramp using the formula PE = mgh, where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp (1.50 m). This will give us the initial potential energy of the car before takeoff.

Next, we need to calculate the minimum kinetic energy required for the car to clear the 20 m horizontal distance. This can be done using the formula KE = 1/2mv^2, where m is the mass of the car and v is the minimum velocity required for the car to clear the distance.

Using the conservation of energy principle, we can equate the initial potential energy to the minimum kinetic energy required. This will give us the minimum velocity (v) needed for the car to successfully jump over the eight cars.

We also need to take into account the angle of the ramp. Since the ramp is tilted upward at a 10° angle, the horizontal velocity of the car will be less than the minimum velocity calculated above. We can use trigonometry to calculate the horizontal velocity (vx) using the formula vx = vcosθ, where θ is the angle of the ramp (10°).

Therefore, the necessary minimum speed for the car to successfully jump over the eight cars is the horizontal velocity (vx) calculated above. This can be found by plugging in the values for m, g, h, and θ into the above equations. I would also suggest verifying your calculations using other equations and principles, such as the laws of motion, to ensure accuracy.

In conclusion, by using the principles of physics and making some assumptions about the mass of the car, we can determine the necessary minimum speed for the car to successfully jump over the eight cars parked below the ramp. I hope this helps you solve the problem. Good luck!