How to Use Symbols to Solve a Ramp Problem?

[Flinze]

Homework Statement

A car is 12 m from the bottom of a ramp that is 8.0 m long at its base and 6.0 m high. The car moves from rest toward the ramp with an acceleration of magnitude 2.5 m/s². At some instant after the car begins moving, a crate is released from rest from some position along the ramp. The crate and car reach the bottom of the ramp at the same instant and at the same speed. (a) At what distance d up the ramp was the crate released? (b) How many seconds after the car started was the crate released?

Homework Equations

x(t) = x_i + v_x,i * t + 1/2a_x²*t²
v_f²=v_i² + 2ad
v(t) = v + at

The Attempt at a Solution

I know that the final symbol of this is d=(x_f*a_x)/g*sin(theta) . which comes to be 5.1m for question (a). How does one answer this question through just using symbols, my teacher is not allowing us to plug in numbers on the way, but rather plug in everything in the end. I'm also confused at which equation I should use.

 

[Dr. Courtney]

You need a good diagram to define your coordinate system and symbols.

You also have two moving objects, which means you need to use different equations for the two different objects.

This is an involved problem where you will have more than one equation and more than one step.

Start with a good picture. Think about each object and which equations are needed for its motion.

Then consider which quantity connects the motion of the two objects.

 

[haruspex]

Solving with symbols follows just the same route as solving with numbers, but has many benefits.
A key to using it successfully is not to reuse the same symbol for different variables. Each object has its own acceleration, distance, and travel time, and each of these deserves its own symbol. They happen to start with the same speeds and end with the same speeds in this instance, though. I don't think your teacher will mind your plugging in 0 for the initial speeds straight away.