(Logic - Medium) The Bridge

Four friends on a hiking trip come across a bright they need to cross. The bridge is old and narrow, and thus it only permits two people to cross at a time. It is dark out and a flashlight is needed to cross the bridge, but the group only has one flashlight.

Each person crosses the bridge at different speeds and when two go together the faster one needs to adapt for the slower one (otherwise they can't share the light). The first person, Greg, needs 10 minutes to cross the bridge. The second, Marcia, needs 5 minutes. The third, Peter, need 2 minutes, and the fastest one, Jan, needs only 1 minute.

What is the shortest time that the group can take to cross the bridge?

(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?