Answer:
f = 5 cm
Explanation:
using the thin lens equation, given as follows:

where,
f = focal length = ?
do = the distance of object from lens = 20 cm
di = the distance of image from lens = 6.6667 cm
Therefore,

<u>f = 5 cm</u>
Answer:
The distance traveled by the balloon is 10.77 m
Explanation:
velocity of the ball,
= 2 m/s south
velocity of the air,
= 5 m/s west
To determine the distance the balloon will travel after 2 seconds, first determine the resultant velocity of the balloon.
| 2m/s
|
|
↓
5m/s ←------------------
the two velocities forms a right angled triangle and the resultant will be the hypotenuses side of the triangle.
R² = 5² + 2²
R² = 29
R = √29
R = 5.385 m/s
The distance traveled by the balloon is calculated as;
d = R x t
where;
t is time of the motion = 2 seconds
d = 5.385 x 2
d = 10.77 m
Therefore, the distance traveled by the balloon is 10.77 m.
To solve this problem it is necessary to apply the concepts related to Normal Force, frictional force, kinematic equations of motion and Newton's second law.
From the kinematic equations of motion we know that the relationship of acceleration, velocity and distance is given by

Where,
Final velocity
Initial Velocity
a = Acceleration
x = Displacement
Acceleration can be expressed in terms of the drag coefficient by means of
Frictional Force
Force by Newton's second Law
Where,
m = mass
a= acceleration
Kinetic frictional coefficient
g = Gravity
Equating both equation we have that



Therefore,


Re-arrange to find x,

The distance traveled by the car depends on the coefficient of kinetic friction, acceleration due to gravity and initial velocity, therefore the three cars will stop at the same distance.
P1v1/t1 = p2v2/t2
p1=p2, v1=.2, t1=333, t2=533
we can find v2 from this
be aware, temperature must be in Kelvin.
You have to solve this by using the equations of motion:
u=3
v=0
s=2.5
a=?
v^2=u^2+2as
0=9+5s
Giving a=-1.8m/s^2
Then using the equation:
F=ma
F is the frictional force as there is no other force acting and its negative as its in the opposite direction to the direction of motion.
-F=25(-1.8)
F=45N
Then use the formula:
F=uR
Where u is the coefficient of friction, R is the normal force and F is the frictional force.
45=u(25g)
45=u(25*10)
Therefore, the coefficient of friction is 0.18
Hope that helps