(Physics - Easy) Traffic Intersection Accident

You've been hired to confirm the witness reports of a traffic accident case. 

Reports say that the 3-ton truck was headed eastbound at 60 MPH. The driver didn't see the light and ran the red. Witnesses then say it collided with a larger 8-ton delivery van going northbound at 35 MPH.

If that's so, what should be the final direction and speed of the allegedly guilty truck?

(Fluids - Medium) Coffee & Alcohol...Jumpstart Your Day!

A Quick Primer

Review of Specific Gravity: It's a dimensionless ratio of the density of a substance over a standard reference density, usually water. (Cool fact: specific gravity is used to classify beer types!)

Review of Specific Volume:

It's just flipped - the reciprocal.


The Problem

Let's start the day off with some coffee & alcohol. 

You have 400 grams of coffee, and decide to mix it up with 150 g of Amaretto (a tasty almond-flavored liqueur). Coffee has a density of 1000 kg/m3, while Amaretto has a specific gravity of 1.08.

Now stir & mix homogeneously.

                                                         (Ignore the cream & nuts)

                                                         (Ignore the cream & nuts)

But wait! Before imbibing, what's the specific volume of the resulting mixture?

 
A) 0.98 cm3/gram
B) 1.021 cm3/gram
C) 1.926 cm3/gram
D) Wheeeeeeee! Coffee gone!

Use latex to write equations.

Necessary Disclaimer: LEARNerds does not condone the consumption of alcohol as a way to jumpstart your day. However, we do condone supporting us with a LEARNerds premium subscription!

(Physics - Medium) Spring-loaded Toy Dart Gun

A spring-loaded toy dart gun is used to shoot a dart straight up in the air. The dart reaches a maximum height hmax. Afterwards, the same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. Neglecting friction and assuming an ideal spring...

How far up does the dart go this time?

(Physics - Easy) Work While You Work

While working out, you pick up a 10 kg weight from rest on the ground and lift it to a height of 2 meters above the ground and hold it there at rest. Assume $ g = 10 m/s^{2} $ .

How much work do you do on the weight in moving it?

(Math - Medium) The Trouble With Tribbles...Exponential Growth

Uh-oh. You're a starship captain returning back to your ship from a well-needed leave, and your first mate's just informed you that there's been a Tribble outbreak. (Tribbles are cute, furry little things that multiply magnitudes faster than rabbits.)

The first Tribble was brought on-board 3 days ago, and it only takes one of them to tango (translation: breed). In the first 12 hours, the original Tribble gave birth to 10 Tribbles. Assuming exponential growth, about how many of these things are now on your ship?


      72
      1339
      1,771,561
      8,561,283