Relative velocities and displacement
In these questions, you have to find the velocity and the displacement of a bird relative to the ground,
when it is actually flying relative to the wind.
Flying in a side wind
–1
A bird flies at a steady speed of 3 m s through the air. It is pointing in the direction due north.
–1
However, there is a wind blowing from west to east at a speed of 2 m s .
1.
What is the velocity of the bird relative to the ground?
2.
What is the displacement of the bird, relative to its starting point, after it has flown for
20 seconds?
3.
In what direction should the bird point if it is to travel in a northerly direction?
Try these calculations
Graph paper is needed for some. These questions are all based on the connection between speed,
distance and time. Answer in the spaces provided:
Hints
In these questions it is useful to remember that:
– if an object is accelerating steadily from rest its average speed is half the maximum speed
– and that distance travelled = average speed x time
1.
You are watching a batsman hit a cricket ball. If 0.375 s passes between the time you see him
strike the ball and the time you hear the sound of this, how far from the batsman are you
–1
sitting? The speed of sound in air is 340 m s . (The speed of light is nearly a million times
bigger than this, so you see the bat hit the ball more or less at the instant it occurs.)
2.
A girl diving from a 15 m platform wishes to know how fast she enters the water. She is in the
air for 1.75 s and dives from rest (with an initial speed of zero). What can you tell her about
her entry speed?
3.
An experiment performed on the Moon finds that a feather falls 20.75 m from rest in 5 s. What
is its speed as it hits the Moon's surface?
4.
The sketch graph shown represents the variation in vertical height with time for a ball thrown
upwards and returning to the thrower.
time
From this graph sketch a velocity–time graph.
5.
–1
In a Tour de France time trial a cyclist is able to reach a top speed of 100 km h by starting
from rest and pedalling flat out for a distance of 3 km. If the rate at which the cyclist's speed
changes is uniform, how long will this take?
Think carefully, and calculate a little.
Two speeds, one principle.
Travelling slowly, at about 5 miles an hour, the retarding forces acting on a cyclist are about 5 N.
1.
What propulsive force must the cyclist provide to travel at constant speed?
2.
How much energy does the cyclist have to provide to cover 5 m?
At a higher speed, nearly 10 mph the retarding forces are much larger, nearly 8 N.
3.
Write down the propulsive force required at this speed.
4.
Calculate the energy the cyclist must provide every to cover 5 m at this constant speed.
Climbing a hill at a steady speed of 5 mph the cyclist finds herself perspiring rather more than on the
flat. The mass of the cycle plus cyclist is 80 kg. The ergometer pedals fitted report the energy
supplied to the bicycle as 185 J to cover a 5 m stretch of road.
5.
How much energy is used to lift the cyclist uphill?
6.
How much height does she gain in travelling along the 5 m stretch of road?
1.
Convert 25 mA to A
2.
Convert 0.50 A to mA
3.
A torch bulb passes a current of 120 mA.
(a)
How many coulombs of charge flow through the lamp in 1 minute?
(b)
How many coulombs of charge flow through the lamp in 1 hour?
(c)
How many electrons leave the negative terminal of the cell each second?
4.
A car battery is rated as 36 A h. In principle this means it could pass a current of 1 A for 36 h
before it runs down. How much charge passes through the battery if it is completely run
down?
The table shows the how the current through a resistor of nominal value 4.7 k changes with the pd
The resistor is designed to have a power dissipation of 1 W.
pd / V
5.0
10.0
20.0
30.0
40.0
50.0
current / mA
1.06
2.13
4.25
6.22
7.91
9.41
1.
Plot a graph from the data and give a possible explanation for the shape of the graph.
2.
Use the graph to find the resistance of the resistor for small applied pds.
3.
What is the resistance when the applied pd is 50 V?
Take c = 3.0  108 m s-1 in air
1.
The speed of light in a certain glass is 1.8  10 8 m s-1 . What is the refractive index of the
glass?
2.
The refractive index of diamond is 2.4. What is the speed of light in diamond?
3.
The refractive index changes with the colour of the light leading to dispersion. If the refractive
index for blue light in a certain glass is 1.639 and for red light is 1.621, calculate the angle
between the rays if they were both incident at 50 o.
4.
Find the relative refractive index from glass to water if the absolute indices are 1.5 and 1.3
respectively.
1
Complete the following nuclear equations. In each case describe the decay process:
131
53 I

Xe 
67
0
31Ga  1e
11
6C

99m
43Tc

0
1e
Zn
B  01e

Tc   .