Physics Check
posted by Ariel on .
Since I've been waiting to get my answers checked for my submission #2, I moved on to my submission #3 and I need some questions checked for my submission #3 please.
1.)If a blue car drives 10km/h across the deck of an ocean liner that is traveling at 90km/h, what is the blue car's speed relative to the surface of the water when it drives toward the front of the ocean liner?
a)10 km/h
b)80 km/h
c)90 km/h
=d)100 km/h
2.)A motorboat travels at a speed of 40 km/h relative to the surface of the water. If it travels upstream against a current of 12 km/h what is the boats speed relative to the shore?
a)3.3 km/h
=b)28 km/h
c)40 km/h
d)52 km/h
3.)An airplane flies north at a speed of 150 km/h relative to the air through which it flies. If there is a tail wind of 50 km/h, what is the plane's velocity relative to the ground?
a)3 km/h north
=b)100 km/h north
c)150 km/h north
d)200 km/h north
4.)A plane flying 100km/h due north encounters a crosswind of 100km/h "from the east" (i.e. blowing westward). What then, is the plane's velocity relative to the ground?
a)141.4 km/h northeast
=b)141.4 km/h northwest
c)100 km/h northeast
d)100 km/h northwest
5.)A bullet is shot from a rifle aimed horizontally at the same time a bullet is dropped from the same height as the gun's barrel. Which bullet hits the ground first?
a)The fired bullet
=b)The dropped bullet
c)Both bullets the ground at the same time
6.)A car drives off a vertical cliff that is 122.5m tall. If the car lands 100m from the base of the cliff what was the cars speed as it drove off the cliff.
a)20m/s
=b)22m/s
c)24m/s
d)26m/s
(#6 I just really guessed because I don't know what to do so I just 122.5100=22.5 so I just stuck with that.)

#1 correct
#2 correct
#3 wrong
#4 correct
#5 wrong

#6
find t in seconds:
122.5m = (0.5)(g)(t^2)
122.5m = (0.5)(9.8m/s^2)t^2
reducing...
25s^2 = t^2
t = +5 seconds and t = 5 seconds
Disregard the negative time.
That is how long it took to fall 122.5m.
So, if the car traveled horizontally 100m in 5 seconds, speed is 100m/5s = 20m/s which is the answer a. 
A more complete explanation...
The car is traveling horizontally at a constant speed. When it drives off the cliff, it keeps going at the same speed (disregarding friction) until it is stopped by hitting the ground. A forumla for (d) distance traveled with constant acceleration, no initial vertical velocity is:
d = (1/2)(a)(t^2)
where a is the acceleration and t is the time. The acceleration due to gravity is about 9.8m/s^2.
d is given as 122.5m.
Once the falling time is found that can be plugged into the formula for speed.
In this case it took 5 seconds to fall, and the car traveled 100m in that time. 
In number 5 both bullets fall at the same rate. The horizontal problem has nothing to do with the vertical problem except that the time in the air is the same.

Thanks:)

A motorboat travels at a speed of 40 km/h relative to the surface of the water. If it travels upstream against a current of 12 km/h what is the boats speed relative to the shore?

An airplane flies north at a speed of 150 km/h relative to the air through which it flies. If there is a tail wind of 50 km/h, what is the plane's velocity relative to the ground?

.)An airplane flies north at a speed of 150 km/h relative to the air through which it flies. If there is a tail wind of 50 km/h, what is the plane's velocity relative to the ground?
200 km/h north 
.)An airplane flies north at a speed of 150 km/h relative to the air through which it flies. If there is a tail wind of 50 km/h, what is the plane's velocity relative to the ground?
150 km/h 
who really cares?